In this article, we will analyze how converting common fractions to decimals, and also consider the reverse process - the conversion of decimal fractions to ordinary fractions. Here we will voice the rules for inverting fractions and give detailed solutions to typical examples.

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Converting common fractions to decimals

Let us denote the sequence in which we will deal with converting common fractions to decimals.

First, we will look at how to represent ordinary fractions with denominators 10, 100, 1000, ... as decimal fractions. This is because decimal fractions are essentially a compact form of ordinary fractions with denominators 10, 100, ....

After that, we will go further and show how any ordinary fraction (not only with denominators 10, 100, ...) can be written as a decimal fraction. With this conversion of ordinary fractions, both finite decimal fractions and infinite periodic decimal fractions are obtained.

Now about everything in order.

Converting ordinary fractions with denominators 10, 100, ... to decimal fractions

Some regular fractions need "preliminary preparation" before converting to decimals. This applies to ordinary fractions, the number of digits in the numerator of which is less than the number of zeros in the denominator. For example, the common fraction 2/100 must first be prepared for conversion to a decimal fraction, but the fraction 9/10 does not need to be prepared.

The “preliminary preparation” of correct ordinary fractions for conversion to decimal fractions consists in adding so many zeros to the left in the numerator so that the total number of digits there becomes equal to the number of zeros in the denominator. For example, a fraction after adding zeros will look like .

After preparing the correct ordinary fraction, you can begin to convert it to a decimal fraction.

Let's give rule for converting a proper common fraction with a denominator of 10, or 100, or 1,000, ... into a decimal fraction. It consists of three steps:

• write down 0 ;
• put a decimal point after it;
• write down the number from the numerator (together with added zeros, if we added them).

Consider the application of this rule in solving examples.

Example.

Convert the proper fraction 37/100 to decimal.

Decision.

The denominator contains the number 100, which has two zeros in its entry. The numerator contains the number 37, there are two digits in its record, therefore, this fraction does not need to be prepared for conversion to a decimal fraction.

Now we write 0, put a decimal point, and write the number 37 from the numerator, while we get the decimal fraction 0.37.

Answer:

0,37 .

To consolidate the skills of translating regular ordinary fractions with numerators 10, 100, ... into decimal fractions, we will analyze the solution of another example.

Example.

Write the proper fraction 107/10,000,000 as a decimal.

Decision.

The number of digits in the numerator is 3, and the number of zeros in the denominator is 7, so this ordinary fraction needs to be prepared for conversion to decimal. We need to add 7-3=4 zeros to the left in the numerator so that the total number of digits there becomes equal to the number of zeros in the denominator. We get .

It remains to form the desired decimal fraction. To do this, firstly, we write down 0, secondly, we put a comma, thirdly, we write down the number from the numerator together with zeros 0000107 , as a result we have a decimal fraction 0.0000107 .

Answer:

0,0000107 .

Improper common fractions do not need preparation when converting to decimal fractions. The following should be adhered to rules for converting improper common fractions with denominators 10, 100, ... to decimal fractions:

• write down the number from the numerator;
• we separate with a decimal point as many digits on the right as there are zeros in the denominator of the original fraction.

Let's analyze the application of this rule when solving an example.

Example.

Convert improper common fraction 56 888 038 009/100 000 to decimal.

Decision.

Firstly, we write down the number from the numerator 56888038009, and secondly, we separate 5 digits on the right with a decimal point, since there are 5 zeros in the denominator of the original fraction. As a result, we have a decimal fraction 568 880.38009.

Answer:

568 880,38009 .

To convert a mixed number into a decimal fraction, the denominator of the fractional part of which is the number 10, or 100, or 1,000, ..., you can convert the mixed number into an improper ordinary fraction, after which the resulting fraction can be converted into a decimal fraction. But you can also use the following the rule for converting mixed numbers with a denominator of the fractional part 10, or 100, or 1,000, ... into decimal fractions:

• if necessary, we perform “preliminary preparation” of the fractional part of the original mixed number by adding the required number of zeros on the left in the numerator;
• write down the integer part of the original mixed number;
• put a decimal point;
• we write the number from the numerator together with the added zeros.

Let's consider an example, in solving which we will perform all the necessary steps to represent a mixed number as a decimal fraction.

Example.

Convert mixed number to decimal.

Decision.

There are 4 zeros in the denominator of the fractional part, and the number 17 in the numerator, consisting of 2 digits, therefore, we need to add two zeros to the left in the numerator so that the number of characters there becomes equal to the number of zeros in the denominator. By doing this, the numerator will be 0017 .

Now we write down the integer part of the original number, that is, the number 23, put a decimal point, after which we write the number from the numerator together with the added zeros, that is, 0017, while we get the desired decimal fraction 23.0017.

Let's write down the whole solution briefly: .

Undoubtedly, it was possible to first represent the mixed number as an improper fraction, and then convert it to a decimal fraction. With this approach, the solution looks like this:

Answer:

23,0017 .

Converting ordinary fractions to finite and infinite periodic decimal fractions

Not only ordinary fractions with denominators 10, 100, ... can be converted into a decimal fraction, but ordinary fractions with other denominators. Now we will figure out how this is done.

In some cases, the original ordinary fraction is easily reduced to one of the denominators 10, or 100, or 1,000, ... (see the reduction of an ordinary fraction to a new denominator), after which it is not difficult to present the resulting fraction as a decimal fraction. For example, it is obvious that the fraction 2/5 can be reduced to a fraction with a denominator 10, for this you need to multiply the numerator and denominator by 2, which will give a fraction 4/10, which, according to the rules discussed in the previous paragraph, can be easily converted into a decimal fraction 0, 4 .

In other cases, you have to use a different way of converting an ordinary fraction into a decimal, which we will now consider.

To convert an ordinary fraction to a decimal fraction, the numerator of the fraction is divided by the denominator, the numerator is previously replaced by a decimal fraction equal to it with any number of zeros after the decimal point (we talked about this in the section equal and unequal decimal fractions). In this case, division is performed in the same way as division by a column of natural numbers, and a decimal point is placed in the quotient when the division of the integer part of the dividend ends. All this will become clear from the solutions of the examples given below.

Example.

Convert the common fraction 621/4 to decimal.

Decision.

We represent the number in the numerator 621 as a decimal fraction by adding a decimal point and a few zeros after it. To begin with, we will add 2 digits 0, later, if necessary, we can always add more zeros. So, we have 621.00 .

Now let's divide the number 621,000 by 4 by a column. The first three steps are no different from dividing by a column of natural numbers, after which we arrive at the following picture:

So we got to the decimal point in the dividend, and the remainder is different from zero. In this case, we put a decimal point in the quotient, and continue the division by a column, ignoring the commas:

This division is completed, and as a result we got the decimal fraction 155.25, which corresponds to the original ordinary fraction.

Answer:

155,25 .

To consolidate the material, consider the solution of another example.

Example.

Convert the common fraction 21/800 to decimal.

Decision.

To convert this common fraction to a decimal, let's divide the decimal fraction 21,000 ... by 800 by a column. After the first step, we will have to put a decimal point in the quotient, and then continue the division:

Finally, we got the remainder 0, on this the conversion of the ordinary fraction 21/400 to the decimal fraction is completed, and we have come to the decimal fraction 0.02625.

Answer:

0,02625 .

It may happen that when dividing the numerator by the denominator of an ordinary fraction, we never get a remainder of 0. In these cases, the division can be continued as long as desired. However, starting from a certain step, the remainders begin to repeat periodically, while the digits in the quotient also repeat. This means that the original common fraction translates to an infinite periodic decimal. Let's show this with an example.

Example.

Write the common fraction 19/44 as a decimal.

Decision.

To convert an ordinary fraction to a decimal, we perform division by a column:

It is already clear that when dividing, the remainders 8 and 36 began to repeat, while in the quotient the numbers 1 and 8 are repeated. Thus, the original ordinary fraction 19/44 is translated into a periodic decimal fraction 0.43181818…=0.43(18) .

Answer:

0,43(18) .

In conclusion of this paragraph, we will figure out which ordinary fractions can be converted to final decimal fractions, and which ones can only be converted to periodic ones.

Let us have an irreducible ordinary fraction in front of us (if the fraction is reducible, then we first perform the reduction of the fraction), and we need to find out what decimal fraction it can be converted into - finite or periodic.

It is clear that if an ordinary fraction can be reduced to one of the denominators 10, 100, 1000, ..., then the resulting fraction can be easily converted into a final decimal fraction according to the rules discussed in the previous paragraph. But to the denominators 10, 100, 1,000, etc. not all ordinary fractions are given. Only fractions can be reduced to such denominators, the denominators of which are at least one of the numbers 10, 100, ... And what numbers can be divisors of 10, 100, ...? The numbers 10, 100, … will allow us to answer this question, and they are as follows: 10=2 5 , 100=2 2 5 5 , 1 000=2 2 2 5 5 5, … . It follows that the divisors of 10, 100, 1,000, etc. there can only be numbers whose decompositions into prime factors contain only the numbers 2 and (or) 5 .

Now we can make a general conclusion about the conversion of ordinary fractions to decimal fractions:

• if only the numbers 2 and (or) 5 are present in the decomposition of the denominator into prime factors, then this fraction can be converted into a final decimal fraction;
• if, in addition to two and fives, there are other prime numbers in the expansion of the denominator, then this fraction is translated into an infinite decimal periodic fraction.

Example.

Without converting ordinary fractions to decimals, tell me which of the fractions 47/20, 7/12, 21/56, 31/17 can be converted to a final decimal fraction, and which can only be converted to a periodic one.

Decision.

The prime factorization of the denominator of the fraction 47/20 has the form 20=2 2 5 . There are only twos and fives in this expansion, so this fraction can be reduced to one of the denominators 10, 100, 1000, ... (in this example, to the denominator 100), therefore, it can be converted to a final decimal fraction.

The prime factorization of the denominator of the fraction 7/12 has the form 12=2 2 3 . Since it contains a simple factor 3 different from 2 and 5, this fraction cannot be represented as a finite decimal fraction, but can be converted to a periodic decimal fraction.

Fraction 21/56 - contractible, after reduction it takes the form 3/8. The decomposition of the denominator into prime factors contains three factors equal to 2, therefore, the ordinary fraction 3/8, and hence the fraction equal to it 21/56, can be translated into a final decimal fraction.

Finally, the expansion of the denominator of the fraction 31/17 is itself 17, therefore, this fraction cannot be converted to a finite decimal fraction, but it can be converted to an infinite periodic one.

Answer:

47/20 and 21/56 can be converted to a final decimal, while 7/12 and 31/17 can only be converted to a periodic decimal.

Common fractions do not convert to infinite non-repeating decimals

The information of the previous paragraph raises the question: “Can an infinite non-periodic fraction be obtained when dividing the numerator of a fraction by the denominator”?

Answer: no. When translating an ordinary fraction, either a finite decimal fraction or an infinite periodic decimal fraction can be obtained. Let's explain why this is so.

From the divisibility theorem with a remainder, it is clear that the remainder is always less than the divisor, that is, if we divide some integer by an integer q, then only one of the numbers 0, 1, 2, ..., q−1 can be the remainder. It follows that after the column divides the integer part of the numerator of an ordinary fraction by the denominator q, after no more than q steps, one of the following two situations will arise:

• either we get the remainder 0 , this will end the division, and we will get the final decimal fraction;
• or we will get a remainder that has already appeared before, after which the remainders will begin to repeat as in the previous example (since when dividing equal numbers by q, equal remainders are obtained, which follows from the already mentioned divisibility theorem), so an infinite periodic decimal fraction will be obtained.

There can be no other options, therefore, when converting an ordinary fraction to a decimal fraction, an infinite non-periodic decimal fraction cannot be obtained.

It also follows from the reasoning given in this paragraph that the length of the period of a decimal fraction is always less than the value of the denominator of the corresponding ordinary fraction.

Convert decimals to common fractions

Now let's figure out how to convert a decimal fraction to an ordinary one. Let's start by converting final decimals to common fractions. After that, consider the method of inverting infinite periodic decimal fractions. In conclusion, let's say about the impossibility of converting infinite non-periodic decimal fractions into ordinary fractions.

Converting end decimals to common fractions

Getting an ordinary fraction, which is written as a final decimal fraction, is quite simple. The rule for converting a final decimal fraction to an ordinary fraction consists of three steps:

• firstly, write the given decimal fraction into the numerator, having previously discarded the decimal point and all zeros on the left, if any;
• secondly, write one in the denominator and add as many zeros to it as there are digits after the decimal point in the original decimal fraction;
• thirdly, if necessary, reduce the resulting fraction.

Let's consider examples.

Example.

Convert the decimal 3.025 to a common fraction.

Decision.

If we remove the decimal point in the original decimal fraction, then we get the number 3025. It has no zeros on the left that we would discard. So, in the numerator of the required fraction we write 3025.

We write the number 1 in the denominator and add 3 zeros to the right of it, since there are 3 digits in the original decimal fraction after the decimal point.

So we got an ordinary fraction 3 025/1 000. This fraction can be reduced by 25, we get .

Answer:

.

Example.

Convert decimal 0.0017 to common fraction.

Decision.

Without a decimal point, the original decimal fraction looks like 00017, discarding zeros on the left, we get the number 17, which is the numerator of the desired ordinary fraction.

In the denominator we write a unit with four zeros, since in the original decimal fraction there are 4 digits after the decimal point.

As a result, we have an ordinary fraction 17/10,000. This fraction is irreducible, and the conversion of a decimal fraction to an ordinary one is completed.

Answer:

.

When the integer part of the original final decimal fraction is different from zero, then it can be immediately converted to a mixed number, bypassing the ordinary fraction. Let's give rule for converting a final decimal to a mixed number:

• the number before the decimal point must be written as the integer part of the desired mixed number;
• in the numerator of the fractional part, you need to write the number obtained from the fractional part of the original decimal fraction after discarding all zeros on the left in it;
• in the denominator of the fractional part, you need to write the number 1, to which, on the right, add as many zeros as there are digits in the entry of the original decimal fraction after the decimal point;
• if necessary, reduce the fractional part of the resulting mixed number.

Consider an example of converting a decimal fraction to a mixed number.

Example.

Express decimal 152.06005 as a mixed number

Fractions

Attention!
There are additional
material in Special Section 555.
For those who strongly "not very..."
And for those who "very much...")

Fractions in high school are not very annoying. For the time being. Until you come across exponents with rational exponents and logarithms. And there…. You press, you press the calculator, and it shows all the full scoreboard of some numbers. You have to think with your head, like in the third grade.

Let's deal with fractions, finally! Well, how much can you get confused in them!? Moreover, it is all simple and logical. So, what are fractions?

Types of fractions. Transformations.

Fractions are of three types.

1. Common fractions , For example:

Sometimes, instead of a horizontal line, they put a slash: 1/2, 3/4, 19/5, well, and so on. Here we will often use this spelling. The top number is called numerator, lower - denominator. If you constantly confuse these names (it happens ...), tell yourself the phrase with the expression: " Zzzzz remember! Zzzzz denominator - out zzzz u!" Look, everything will be remembered.)

A dash, which is horizontal, which is oblique, means division top number (numerator) to bottom number (denominator). And that's it! Instead of a dash, it is quite possible to put a division sign - two dots.

When the division is possible entirely, it must be done. So, instead of the fraction "32/8" it is much more pleasant to write the number "4". Those. 32 is simply divided by 8.

32/8 = 32: 8 = 4

I'm not talking about the fraction "4/1". Which is also just "4". And if it doesn’t divide completely, we leave it as a fraction. Sometimes you have to do the reverse. Make a fraction from a whole number. But more on that later.

2. Decimals , For example:

It is in this form that it will be necessary to write down the answers to tasks "B".

3. mixed numbers , For example:

Mixed numbers are practically not used in high school. In order to work with them, they must be converted to ordinary fractions. But you definitely need to know how to do it! And then such a number will come across in the puzzle and hang ... From scratch. But we remember this procedure! A little lower.

Most versatile common fractions. Let's start with them. By the way, if there are all sorts of logarithms, sines and other letters in the fraction, this does not change anything. In the sense that everything actions with fractional expressions are no different from actions with ordinary fractions!

Basic property of a fraction.

So let's go! First of all, I will surprise you. The whole variety of fraction transformations is provided by a single property! That's what it's called basic property of a fraction. Remember: If the numerator and denominator of a fraction are multiplied (divided) by the same number, the fraction will not change. Those:

It is clear that you can write further, until you are blue in the face. Do not let sines and logarithms confuse you, we will deal with them further. The main thing to understand is that all these various expressions are the same fraction . 2/3.

And we need it, all these transformations? And how! Now you will see for yourself. First, let's use the basic property of a fraction for fraction abbreviations. It would seem that the thing is elementary. We divide the numerator and denominator by the same number and that's it! It's impossible to go wrong! But... man is a creative being. You can make mistakes everywhere! Especially if you have to reduce not a fraction like 5/10, but a fractional expression with all sorts of letters.

How to reduce fractions correctly and quickly without doing unnecessary work can be found in special Section 555.

A normal student does not bother dividing the numerator and denominator by the same number (or expression)! He just crosses out everything the same from above and below! This is where a typical mistake lurks, a blunder, if you like.

For example, you need to simplify the expression:

There is nothing to think about, we cross out the letter "a" from above and the deuce from below! We get:

Everything is correct. But really you shared the whole numerator and the whole denominator "a". If you are used to just cross out, then, in a hurry, you can cross out the "a" in the expression

and get again

Which would be categorically wrong. Because here the whole numerator on "a" already not shared! This fraction cannot be reduced. By the way, such an abbreviation is, um ... a serious challenge to the teacher. This is not forgiven! Remember? When reducing, it is necessary to divide the whole numerator and the whole denominator!

Reducing fractions makes life a lot easier. You will get a fraction somewhere, for example 375/1000. And how to work with her now? Without a calculator? Multiply, say, add, square!? And if you are not too lazy, but carefully reduce by five, and even by five, and even ... while it is being reduced, in short. We get 3/8! Much nicer, right?

The basic property of a fraction allows you to convert ordinary fractions to decimals and vice versa without calculator! This is important for the exam, right?

How to convert fractions from one form to another.

It's easy with decimals. As it is heard, so it is written! Let's say 0.25. It's zero point, twenty-five hundredths. So we write: 25/100. We reduce (divide the numerator and denominator by 25), we get the usual fraction: 1/4. Everything. It happens, and nothing is reduced. Like 0.3. This is three tenths, i.e. 3/10.

What if integers are non-zero? It's OK. Write down the whole fraction without any commas in the numerator, and in the denominator - what is heard. For example: 3.17. This is three whole, seventeen hundredths. We write 317 in the numerator, and 100 in the denominator. We get 317/100. Nothing is reduced, that means everything. This is the answer. Elementary Watson! From all of the above, a useful conclusion: any decimal fraction can be converted to a common fraction .

But the reverse conversion, ordinary to decimal, some cannot do without a calculator. But you must! How will you write down the answer on the exam!? We carefully read and master this process.

What is a decimal fraction? She has in the denominator always is worth 10 or 100 or 1000 or 10000 and so on. If your usual fraction has such a denominator, there is no problem. For example, 4/10 = 0.4. Or 7/100 = 0.07. Or 12/10 = 1.2. And if in the answer to the task of section "B" it turned out 1/2? What will we write in response? Decimals are required...

We remember basic property of a fraction ! Mathematics favorably allows you to multiply the numerator and denominator by the same number. For anyone, by the way! Except zero, of course. Let's use this feature to our advantage! What can the denominator be multiplied by, i.e. 2 so that it becomes 10, or 100, or 1000 (smaller is better, of course...)? 5, obviously. Feel free to multiply the denominator (this is us necessary) by 5. But, then the numerator must also be multiplied by 5. This is already mathematics demands! We get 1/2 \u003d 1x5 / 2x5 \u003d 5/10 \u003d 0.5. That's all.

However, all sorts of denominators come across. For example, the fraction 3/16 will fall. Try it, figure out what to multiply 16 by to get 100, or 1000... Doesn't work? Then you can simply divide 3 by 16. In the absence of a calculator, you will have to divide in a corner, on a piece of paper, as they taught in elementary grades. We get 0.1875.

And there are some very bad denominators. For example, the fraction 1/3 cannot be turned into a good decimal. Both on a calculator and on a piece of paper, we get 0.3333333 ... This means that 1/3 into an exact decimal fraction does not translate. Just like 1/7, 5/6 and so on. Many of them are untranslatable. Hence another useful conclusion. Not every common fraction converts to a decimal. !

By the way, this is useful information for self-examination. In section "B" in response, you need to write down a decimal fraction. And you got, for example, 4/3. This fraction is not converted to decimal. This means that somewhere along the way you made a mistake! Come back, check the solution.

So, with ordinary and decimal fractions sorted out. It remains to deal with mixed numbers. To work with them, they all need to be converted to ordinary fractions. How to do it? You can catch a sixth grader and ask him. But not always a sixth grader will be at hand ... We will have to do it ourselves. It's not hard. Multiply the denominator of the fractional part by the integer part and add the numerator of the fractional part. This will be the numerator of a common fraction. What about the denominator? The denominator will remain the same. It sounds complicated, but it's actually quite simple. Let's see an example.

Let in the problem you saw with horror the number:

Calmly, without panic, we understand. The whole part is 1. One. The fractional part is 3/7. Therefore, the denominator of the fractional part is 7. This denominator will be the denominator of the ordinary fraction. We count the numerator. We multiply 7 by 1 (the integer part) and add 3 (the numerator of the fractional part). We get 10. This will be the numerator of an ordinary fraction. That's all. It looks even simpler in mathematical notation:

Clearly? Then secure your success! Convert to common fractions. You should get 10/7, 7/2, 23/10 and 21/4.

The reverse operation - converting an improper fraction into a mixed number - is rarely required in high school. Well, if... And if you - not in high school - you can look into the special Section 555. In the same place, by the way, you will learn about improper fractions.

Well, almost everything. You remembered the types of fractions and understood as convert them from one type to another. The question remains: why do it? Where and when to apply this deep knowledge?

I answer. Any example itself suggests the necessary actions. If in the example ordinary fractions, decimals, and even mixed numbers are mixed into a bunch, we translate everything into ordinary fractions. It can always be done. Well, if something like 0.8 + 0.3 is written, then we think so, without any translation. Why do we need extra work? We choose the solution that is convenient us !

If the task is full of decimal fractions, but um ... some kind of evil ones, go to ordinary ones, try it! Look, everything will be fine. For example, you have to square the number 0.125. Not so easy if you have not lost the habit of the calculator! Not only do you need to multiply the numbers in a column, but also think about where to insert the comma! It certainly doesn't work in my mind! And if you go to an ordinary fraction?

0.125 = 125/1000. We reduce by 5 (this is for starters). We get 25/200. Once again on 5. We get 5/40. Oh, it's shrinking! Back to 5! We get 1/8. Easily square (in your mind!) and get 1/64. Everything!

Let's summarize this lesson.

1. There are three types of fractions. Ordinary, decimal and mixed numbers.

2. Decimals and mixed numbers always can be converted to common fractions. Reverse Translation not always available.

3. The choice of the type of fractions for working with the task depends on this very task. If there are different types of fractions in one task, the most reliable thing is to switch to ordinary fractions.

Now you can practice. First, convert these decimal fractions to ordinary ones:

3,8; 0,75; 0,15; 1,4; 0,725; 0,012

You should get answers like this (in a mess!):

On this we will finish. In this lesson, we brushed up on the key points on fractions. It happens, however, that there is nothing special to refresh ...) If someone has completely forgotten, or has not mastered it yet ... Those can go to a special Section 555. All the basics are detailed there. Many suddenly understand everything are starting. And they solve fractions on the fly).

If you like this site...

By the way, I have a couple more interesting sites for you.)

You can practice solving examples and find out your level. Testing with instant verification. Learning - with interest!)

you can get acquainted with functions and derivatives.

Already in elementary school, students are faced with fractions. And then they appear in every topic. It is impossible to forget actions with these numbers. Therefore, you need to know all the information about ordinary and decimal fractions. These concepts are simple, the main thing is to understand everything in order.

Why are fractions needed?

The world around us consists of whole objects. Therefore, there is no need for shares. But everyday life constantly pushes people to work with parts of objects and things.

For example, chocolate consists of several slices. Consider the situation where its tile is formed by twelve rectangles. If you divide it into two, you get 6 parts. It will be well divided into three. But the five will not be able to give a whole number of slices of chocolate.

By the way, these slices are already fractions. And their further division leads to the appearance of more complex numbers.

What is a "fraction"?

This is a number consisting of parts of one. Outwardly, it looks like two numbers separated by a horizontal or slash. This feature is called fractional. The number written on the top (left) is called the numerator. The one on the bottom (right) is the denominator.

In fact, the fractional bar turns out to be a division sign. That is, the numerator can be called a dividend, and the denominator can be called a divisor.

What are the fractions?

In mathematics, there are only two types of them: ordinary and decimal fractions. Schoolchildren get acquainted with the first ones in the elementary grades, calling them simply “fractions”. The second learn in the 5th grade. That's when these names appear.

Common fractions are all those that are written as two numbers separated by a bar. For example, 4/7. Decimal is a number in which the fractional part has a positional notation and is separated from the integer with a comma. For example, 4.7. Students need to be clear that the two examples given are completely different numbers.

Every simple fraction can be written as a decimal. This statement is almost always true in reverse as well. There are rules that allow you to write a decimal fraction as an ordinary fraction.

What subspecies do these types of fractions have?

It is better to start in chronological order, as they are being studied. Common fractions come first. Among them, 5 subspecies can be distinguished.

Correct. Its numerator is always less than the denominator.

Wrong. Its numerator is greater than or equal to the denominator.

Reducible / irreducible. It can be either right or wrong. Another thing is important, whether the numerator and denominator have common factors. If there are, then they are supposed to divide both parts of the fraction, that is, to reduce it.

Mixed. An integer is assigned to its usual correct (incorrect) fractional part. And it always stands on the left.

Composite. It is formed from two fractions divided into each other. That is, it has three fractional features at once.

Decimals have only two subspecies:

final, that is, one in which the fractional part is limited (has an end);

infinite - a number whose digits after the decimal point do not end (they can be written endlessly).

How to convert decimal to ordinary?

If this is a finite number, then an association based on the rule is applied - as I hear, so I write. That is, you need to read it correctly and write it down, but without a comma, but with a fractional line.

As a hint about the required denominator, remember that it is always a one and a few zeros. The latter need to be written as many as the digits in the fractional part of the number in question.

How to convert decimal fractions to ordinary ones if their whole part is missing, that is, equal to zero? For example, 0.9 or 0.05. After applying the specified rule, it turns out that you need to write zero integers. But it is not indicated. It remains to write down only the fractional parts. For the first number, the denominator will be 10, for the second - 100. That is, the indicated examples will have numbers as answers: 9/10, 5/100. Moreover, the latter turns out to be possible to reduce by 5. Therefore, the result for it must be written 1/20.

How to make an ordinary fraction from a decimal if its integer part is different from zero? For example, 5.23 or 13.00108. Both examples read the integer part and write its value. In the first case, this is 5, in the second, 13. Then you need to move on to the fractional part. With them it is necessary to carry out the same operation. The first number has 23/100, the second has 108/100000. The second value needs to be reduced again. The answer is mixed fractions: 5 23/100 and 13 27/25000.

How to convert an infinite decimal to a common fraction?

If it is non-periodic, then such an operation cannot be carried out. This fact is due to the fact that each decimal fraction is always converted to either final or periodic.

The only thing that is allowed to be done with such a fraction is to round it. But then the decimal will be approximately equal to that infinite. It can already be turned into an ordinary one. But the reverse process: converting to decimal - will never give the initial value. That is, infinite non-periodic fractions are not translated into ordinary fractions. This must be remembered.

How to write an infinite periodic fraction in the form of an ordinary?

In these numbers, one or more digits always appear after the decimal point, which are repeated. They are called periods. For example, 0.3(3). Here "3" in the period. They are classified as rational, as they can be converted into ordinary fractions.

Those who have encountered periodic fractions know that they can be pure or mixed. In the first case, the period starts immediately from the comma. In the second, the fractional part begins with any numbers, and then the repetition begins.

The rule by which you need to write an infinite decimal in the form of an ordinary fraction will be different for these two types of numbers. It is quite easy to write pure periodic fractions as ordinary fractions. As with the final ones, they need to be converted: write the period into the numerator, and the number 9 will be the denominator, repeating as many times as there are digits in the period.

For example, 0,(5). The number does not have an integer part, so you need to immediately proceed to the fractional part. Write 5 in the numerator, and write 9 in the denominator. That is, the answer will be the fraction 5/9.

A rule on how to write a common decimal fraction that is a mixed fraction.

Look at the length of the period. So much 9 will have a denominator.

Write down the denominator: first nines, then zeros.

To determine the numerator, you need to write the difference of two numbers. All digits after the decimal point will be reduced, along with the period. Subtractable - it is without a period.

For example, 0.5(8) - write the periodic decimal fraction as a common fraction. The fractional part before the period is one digit. So zero will be one. There is also only one digit in the period - 8. That is, there is only one nine. That is, you need to write 90 in the denominator.

To determine the numerator from 58, you need to subtract 5. It turns out 53. For example, you will have to write 53/90 as an answer.

How are common fractions converted to decimals?

The simplest option is a number whose denominator is the number 10, 100, and so on. Then the denominator is simply discarded, and a comma is placed between the fractional and integer parts.

There are situations when the denominator easily turns into 10, 100, etc. For example, the numbers 5, 20, 25. It is enough to multiply them by 2, 5 and 4, respectively. Only it is necessary to multiply not only the denominator, but also the numerator by the same number.

For all other cases, a simple rule will come in handy: divide the numerator by the denominator. In this case, you may get two answers: a final or a periodic decimal fraction.

Operations with common fractions

Addition and subtraction

Students get to know them earlier than others. And at first the fractions have the same denominators, and then different. General rules can be reduced to such a plan.

Find the least common multiple of the denominators.

Write additional factors to all ordinary fractions.

Multiply the numerators and denominators by the factors defined for them.

Add (subtract) the numerators of fractions, and leave the common denominator unchanged.

If the numerator of the minuend is less than the subtrahend, then you need to find out whether we have a mixed number or a proper fraction.

In the first case, the integer part needs to take one. Add a denominator to the numerator of a fraction. And then do the subtraction.

In the second - it is necessary to apply the rule of subtraction from a smaller number to a larger one. That is, subtract the modulus of the minuend from the modulus of the subtrahend, and put the “-” sign in response.

Look carefully at the result of addition (subtraction). If you get an improper fraction, then it is supposed to select the whole part. That is, divide the numerator by the denominator.

Multiplication and division

For their implementation, fractions do not need to be reduced to a common denominator. This makes it easier to take action. But they still have to follow the rules.

When multiplying ordinary fractions, it is necessary to consider the numbers in the numerators and denominators. If any numerator and denominator have a common factor, then they can be reduced.

Multiply numerators.

Multiply the denominators.

If you get a reducible fraction, then it is supposed to be simplified again.

When dividing, you must first replace division with multiplication, and the divisor (second fraction) with a reciprocal (swap the numerator and denominator).

Then proceed as in multiplication (starting from point 1).

In tasks where you need to multiply (divide) by an integer, the latter is supposed to be written as an improper fraction. That is, with a denominator of 1. Then proceed as described above.



Operations with decimals

Addition and subtraction

Of course, you can always turn a decimal into a common fraction. And act according to the already described plan. But sometimes it is more convenient to act without this translation. Then the rules for their addition and subtraction will be exactly the same.

Equalize the number of digits in the fractional part of the number, that is, after the decimal point. Assign the missing number of zeros in it.

Write fractions so that the comma is under the comma.

Add (subtract) like natural numbers.

Remove the comma.

Multiplication and division

It is important that you do not need to append zeros here. Fractions are supposed to be left as they are given in the example. And then go according to plan.

For multiplication, you need to write fractions one under the other, not paying attention to commas.

Multiply like natural numbers.

Put a comma in the answer, counting from the right end of the answer as many digits as they are in the fractional parts of both factors.

To divide, you must first convert the divisor: make it a natural number. That is, multiply it by 10, 100, etc., depending on how many digits are in the fractional part of the divisor.

Multiply the dividend by the same number.

Divide a decimal by a natural number.

Put a comma in the answer at the moment when the division of the whole part ends.



What if there are both types of fractions in one example?

Yes, in mathematics there are often examples in which you need to perform operations on ordinary and decimal fractions. There are two possible solutions to these problems. You need to objectively weigh the numbers and choose the best one.

First way: represent ordinary decimals

It is suitable if, when dividing or converting, final fractions are obtained. If at least one number gives a periodic part, then this technique is prohibited. Therefore, even if you do not like working with ordinary fractions, you will have to count them.

The second way: write decimal fractions as ordinary

This technique is convenient if there are 1-2 digits in the part after the decimal point. If there are more of them, a very large ordinary fraction can turn out and decimal entries will allow you to calculate the task faster and easier. Therefore, it is always necessary to soberly evaluate the task and choose the simplest solution method.

Then press the buttons, and the task is completed. As a result, you will get either an integer or a decimal fraction. A decimal fraction can have a long remainder after . In this case, the fraction must be rounded to a certain digit you need using rounding (numbers up to 5 are rounded down, from 5 inclusive and more - up).

If the calculator is not at hand, but you will have to. Write the numerator of a fraction with a denominator, between them a little corner, meaning. For example, convert the fraction 10/6 to a number. To begin with, divide 10 by 6. It turns out 1. Write down the result in a corner. Multiply 1 by 6, you get 6. Subtract 6 from 10. You get a remainder of 4. The remainder must be divided by 6 again. Add 0 to 4, and divide 40 by 6. You get 6. Write 6 in the result, after the decimal point. Multiply 6 by 6. You get 36. Subtract 36 from 40. You get the remainder again 4. Then you can not continue, because it becomes obvious that the result will be the number 1.66 (6). Round the given fraction to the digit you need. For example, 1.67. This is the final result.

Related article

Sources:

• converting fractions to whole numbers

Fractions are needed to denote numbers that consist of one or more parts of the unit. The term "fraction" comes from the Latin fractura, which means "to crush, break". There are ordinary and decimal fractions. At the same time, in ordinary fractions, a unit can be divided into any number of parts, and in decimal fractions, this number must be a multiple of 10. Any fraction can be both ordinary and decimal.

You will need

• To calculate the result, you will need a calculator or a piece of paper and a pen.

Instruction

So, for starters, take an ordinary fraction and divide it into parts. For example, 2 1/8, in which 2 is an integer part, and 1/8 is a fraction. From it you can see that the number was divided by 8, but only one was taken. The part that was taken is the numerator, and the number of parts into which it is divided is the denominator.

note

Often there are fractions that cannot be fully converted to decimals. This is where rounding comes in handy. If you want to round to thousandths, then look at the fourth number after the decimal point. If it is less than 5, then write down in response, the first three digits after the decimal point without change, otherwise, one must be added to the last digit of the three. For example, 0.89643123 can be written as 0.896, but 0.89663123 can be written as 0.897.

Helpful advice

If you calculate the result manually, then before dividing the fraction, it is better to reduce it as much as possible, and also to select whole parts from it.

Sources:

• how to convert fractions

Fraction is one of the elements of formulas for the input of which in the word processor Word there is a Microsoft Equation tool. With it, you can enter any complex mathematical or physical formulas, equations and other elements that include special characters.

Instruction

To launch the Microsoft Equation tool, you need to go to the address: "Insert" -> "Object", in the dialog box that opens, on the first tab from the list, select Microsoft Equation and click "OK" or double-click on the selected item. After launching the editor, a toolbar will open in front of you and an input field will be displayed: a rectangle in a dotted one. The toolbar is divided into sections, each of which contains a set of action signs or expressions. When you click on one of the sections, a list of the tools in it will expand. From the list that opens, select the desired symbol and click on it. Once selected, the specified character will appear in a selected rectangle in the document.

The section that contains elements for writing fractions is located in the second line of the toolbar. When you hover your mouse cursor over it, you will see the tooltip "Fraction and Radical Patterns". Click a section once and expand the list. The drop-down menu has templates for horizontal and oblique fractions. Among the options that appear, you can choose the one that suits your task. Click on the desired option. After clicking, in the input field that opened in the document, a fraction symbol and places for entering the numerator and denominator, framed by a dotted line, will appear. The default cursor is automatically placed in the field for entering the numerator. Enter the numerator. In addition to numbers, you can also enter symbols, letters, or action signs. They can be entered both from the keyboard and from the corresponding sections of the Microsoft Equation toolbar. After the numerator water, press the TAB key to move to the denominator. You can also go by clicking the mouse in the field for entering the denominator. Once written, click with the mouse pointer anywhere in the document, the toolbar will close, the fraction input will be completed. To edit , double-click on it with the left mouse button.

If, when you open the menu "Insert" -> "Object", you did not find the Microsoft Equation tool in the list, you need to install it. Run the installation disc, disc image, or Word distribution file. In the installer window that appears, select "Add or remove components. Adding or removing individual components" and click "Next". In the next window, check the item "Advanced application settings". Click next. In the next window, find the list item "Office Tools" and click on the plus sign on the left. In the expanded list, we are interested in the item "Formula Editor". Click on the icon next to "Formula Editor" and, in the menu that opens, click "Run from computer". After that, click "Update" and wait until the required component is installed.

We have already said that fractions are ordinary and decimal. At the moment, we have studied ordinary fractions a little. We learned that there are regular fractions and improper fractions. We also learned that ordinary fractions can be reduced, added, subtracted, multiplied and divided. And we also learned that there are so-called mixed numbers, which consist of an integer and a fractional part.

We have not yet fully studied ordinary fractions. There are many subtleties and details that should be discussed, but today we will begin to study decimal fractions, since ordinary and decimal fractions often have to be combined. That is, when solving problems, you have to use both types of fractions.

This lesson may seem complicated and incomprehensible. It's quite normal. These kinds of lessons require that they be studied and not skimmed over.

Lesson content

Expressing quantities in fractional form

Sometimes it is convenient to show something in fractional form. For example, one tenth of a decimeter is written like this:

This expression means that one decimeter was divided into ten parts, and one part was taken from these ten parts:

As you can see in the figure, one tenth of a decimeter is one centimeter.

Consider the following example. Show 6 cm and another 3 mm in centimeters in fractional form.

So, it is required to express 6 cm and 3 mm in centimeters, but in fractional form. We already have 6 whole centimeters:

but there are still 3 millimeters left. How to show these 3 millimeters, while in centimeters? Fractions come to the rescue. 3 millimeters is one third of a centimeter. And the third part of a centimeter is written as cm

A fraction means that one centimeter was divided into ten equal parts, and three parts were taken from these ten parts (three out of ten).

As a result, we have six whole centimeters and three tenths of a centimeter:

In this case, 6 shows the number of whole centimeters, and the fraction shows the number of fractional centimeters. This fraction is read as "six point and three tenths of a centimeter".

Fractions, in the denominator of which there are numbers 10, 100, 1000, can be written without a denominator. First write the integer part, and then the numerator of the fractional part. The integer part is separated from the numerator of the fractional part by a comma.

For example, let's write without a denominator. To do this, we first write down the whole part. The integer part is the number 6. We write down this number first:

The whole part is recorded. Immediately after writing the whole part, put a comma:

And now we write down the numerator of the fractional part. In a mixed number, the numerator of the fractional part is the number 3. We write the three after the decimal point:

Any number that is represented in this form is called decimal.

Therefore, you can show 6 cm and another 3 mm in centimeters using a decimal fraction:

6.3 cm

It will look like this:

In fact, decimals are the same common fractions and mixed numbers. The peculiarity of such fractions is that the denominator of their fractional part contains the numbers 10, 100, 1000 or 10000.

Like a mixed number, a decimal has an integer part and a fractional part. For example, in a mixed number, the integer part is 6 and the fractional part is .

In the decimal fraction 6.3, the integer part is the number 6, and the fractional part is the numerator of the fraction, that is, the number 3.

It also happens that ordinary fractions in the denominator of which the numbers 10, 100, 1000 are given without an integer part. For example, a fraction is given without an integer part. To write such a fraction as a decimal, first write down 0, then put a comma and write down the numerator of the fractional part. A fraction without a denominator would be written like this:

Reads like "zero point five tenths".

Convert mixed numbers to decimals

When we write mixed numbers without a denominator, we are converting them to decimals. When converting ordinary fractions to decimal fractions, there are a few things you need to know, which we'll talk about now.

After the integer part is written, it is imperative to count the number of zeros in the denominator of the fractional part, since the number of zeros in the fractional part and the number of digits after the decimal point in the decimal fraction must be the same. What does it mean? Consider the following example:

At first

And you could immediately write down the numerator of the fractional part and the decimal fraction is ready, but you must definitely count the number of zeros in the denominator of the fractional part.

So, we count the number of zeros in the fractional part of the mixed number. The denominator of the fractional part has one zero. So in the decimal fraction after the decimal point there will be one digit and this figure will be the numerator of the fractional part of the mixed number, that is, the number 2

Thus, the mixed number, when translated into a decimal fraction, becomes 3.2.

This decimal is read like this:

"Three whole two tenths"

"Tenths" because the fractional part of the mixed number contains the number 10.

Example 2 Convert mixed number to decimal.

We write down the whole part and put a comma:

And you could immediately write down the numerator of the fractional part and get the decimal fraction 5.3, but the rule says that after the decimal point there should be as many digits as there are zeros in the denominator of the fractional part of the mixed number. And we see that there are two zeros in the denominator of the fractional part. So in our decimal fraction after the decimal point there should be two digits, not one.

In such cases, the numerator of the fractional part needs to be slightly modified: add a zero before the numerator, that is, before the number 3

Now you can convert this mixed number to a decimal. We write down the whole part and put a comma:

And write the numerator of the fractional part:

The decimal fraction 5.03 reads like this:

"Five point three hundredths"

"Hundredths" because the denominator of the fractional part of the mixed number is the number 100.

Example 3 Convert mixed number to decimal.

From the previous examples, we learned that in order to successfully convert a mixed number to a decimal, the number of digits in the numerator of the fractional part and the number of zeros in the denominator of the fractional part must be the same.

Before converting a mixed number into a decimal fraction, its fractional part needs to be slightly modified, namely, to make sure that the number of digits in the numerator of the fractional part and the number of zeros in the denominator of the fractional part are the same.

First of all, we look at the number of zeros in the denominator of the fractional part. We see that there are three zeros:

Our task is to organize three digits in the numerator of the fractional part. We already have one digit - this is the number 2. It remains to add two more digits. They will be two zeros. Add them before the number 2. As a result, the number of zeros in the denominator and the number of digits in the numerator will become the same:

Now we can turn this mixed number into a decimal. We write down the whole part first and put a comma:

and immediately write down the numerator of the fractional part

3,002

We see that the number of digits after the decimal point and the number of zeros in the denominator of the fractional part of the mixed number are the same.

The decimal 3.002 reads like this:

"Three whole, two thousandths"

"Thousandths" because the denominator of the fractional part of the mixed number is the number 1000.

Converting common fractions to decimals

Ordinary fractions, in which the denominator is 10, 100, 1000 or 10000, can also be converted to decimal fractions. Since an ordinary fraction does not have an integer part, first write down 0, then put a comma and write down the numerator of the fractional part.

Here, too, the number of zeros in the denominator and the number of digits in the numerator must be the same. Therefore, you should be careful.

Example 1

The integer part is missing, so first we write 0 and put a comma:

Now look at the number of zeros in the denominator. We see that there is one zero. And the numerator has one digit. So you can safely continue the decimal fraction by writing the number 5 after the decimal point

In the resulting decimal fraction 0.5, the number of digits after the decimal point and the number of zeros in the denominator of the fraction are the same. So the fraction is correct.

The decimal fraction 0.5 reads like this:

"Zero point, five tenths"

Example 2 Convert common fraction to decimal.

The whole part is missing. We write 0 first and put a comma:

Now look at the number of zeros in the denominator. We see that there are two zeros. And the numerator has only one digit. To make the number of digits and the number of zeros the same, add one zero in the numerator before the number 2. Then the fraction will take the form . Now the number of zeros in the denominator and the number of digits in the numerator are the same. So you can continue the decimal:

In the resulting decimal fraction 0.02, the number of digits after the decimal point and the number of zeros in the denominator of the fraction are the same. So the fraction is correct.

The decimal fraction 0.02 reads like this:

"Zero point, two hundredths."

Example 3 Convert common fraction to decimal.

We write 0 and put a comma:

Now we count the number of zeros in the denominator of the fraction. We see that there are five zeros, and there is only one digit in the numerator. To make the number of zeros in the denominator and the number of digits in the numerator the same, you need to add four zeros in the numerator before the number 5:

Now the number of zeros in the denominator and the number of digits in the numerator are the same. So you can continue the decimal. We write down the numerator of the fraction after the decimal point

In the resulting decimal fraction 0.00005, the number of digits after the decimal point and the number of zeros in the denominator of the fraction are the same. So the fraction is correct.

The decimal fraction 0.00005 reads like this:

"Zero point, five hundred-thousandths."

Convert improper fractions to decimals

An improper fraction is a fraction whose numerator is greater than the denominator. There are improper fractions that have the numbers 10, 100, 1000 or 10000 in the denominator. Such fractions can be converted to decimal fractions. But before converting to a decimal fraction, such fractions must have an integer part.

Example 1

The fraction is an improper fraction. To convert such a fraction to a decimal fraction, you must first select its integer part. We recall how to select the whole part of improper fractions. If you forgot, we advise you to return to and study it.

So, let's select the integer part in the improper fraction. Recall that a fraction means division - in this case, dividing the number 112 by the number 10

Let's look at this picture and assemble a new mixed number, like a children's construction set. The number 11 will be the integer part, the number 2 will be the numerator of the fractional part, the number 10 will be the denominator of the fractional part.

We got a mixed number. Let's convert it to a decimal. And we already know how to translate such numbers into decimal fractions. First we write down the whole part and put a comma:

Now we count the number of zeros in the denominator of the fractional part. We see that there is one zero. And the numerator of the fractional part has one digit. This means that the number of zeros in the denominator of the fractional part and the number of digits in the numerator of the fractional part are the same. This gives us the opportunity to immediately write the numerator of the fractional part after the decimal point:

In the resulting decimal fraction 11.2, the number of digits after the decimal point and the number of zeros in the denominator of the fraction are the same. So the fraction is correct.

This means that an improper fraction, when converted to a decimal fraction, turns into 11.2

Decimal 11.2 reads like this:

"Eleven whole, two tenths."

Example 2 Convert improper fraction to decimal.

This is an improper fraction because the numerator is greater than the denominator. But it can be converted to a decimal fraction, since the denominator is the number 100.

First of all, we select the integer part of this fraction. To do this, divide 450 by 100 by a corner:

Let's collect a new mixed number - we get . And we already know how to translate mixed numbers into decimal fractions.

We write down the whole part and put a comma:

Now we count the number of zeros in the denominator of the fractional part and the number of digits in the numerator of the fractional part. We see that the number of zeros in the denominator and the number of digits in the numerator are the same. This gives us the opportunity to immediately write the numerator of the fractional part after the decimal point:

In the resulting decimal fraction 4.50, the number of digits after the decimal point and the number of zeros in the denominator of the fraction are the same. So the fraction is translated correctly.

So the improper fraction, when translated into a decimal fraction, turns into 4.50

When solving problems, if there are zeros at the end of the decimal fraction, they can be discarded. Let's drop the zero in our answer. Then we get 4.5

This is one of the interesting features of decimals. It lies in the fact that the zeros that are at the end of the fraction do not give this fraction any weight. In other words, the decimals 4.50 and 4.5 are equal. Let's put an equal sign between them:

4,50 = 4,5

The question arises: why is this happening? After all, 4.50 and 4.5 look like different fractions. The whole secret lies in the basic property of the fraction, which we studied earlier. We will try to prove why the decimal fractions 4.50 and 4.5 are equal, but after studying the next topic, which is called "converting a decimal fraction to a mixed number."

Decimal to mixed number conversion

Any decimal fraction can be converted back to a mixed number. To do this, it is enough to be able to read decimal fractions. For example, let's convert 6.3 to a mixed number. 6.3 is six whole points and three tenths. We write down six integers first:

and next three tenths:

Example 2 Convert decimal 3.002 to mixed number

3.002 is three integers and two thousandths. Write down three integers first.

and next we write two thousandths:

Example 3 Convert decimal 4.50 to mixed number

4.50 is four point and fifty hundredths. Write down four integers

and next fifty hundredths:

By the way, let's remember the last example from the previous topic. We said that the decimals 4.50 and 4.5 are equal. We also said that zero can be discarded. Let's try to prove that decimal 4.50 and 4.5 are equal. To do this, we convert both decimal fractions to mixed numbers.

After converting to a mixed number, the decimal 4.50 becomes , and the decimal 4.5 becomes

We have two mixed numbers and . Convert these mixed numbers to improper fractions:

Now we have two fractions and . It is time to remember the basic property of a fraction, which says that when multiplying (or dividing) the numerator and denominator of a fraction by the same number, the value of the fraction does not change.

Let's divide the first fraction by 10

Received, and this is the second fraction. So and are equal to each other and equal to the same value:

Try dividing 450 by 100 first on a calculator, and then 45 by 10. A funny thing will work out.

Convert decimal to common fraction

Any decimal fraction can be converted back to a common fraction. To do this, again, it is enough to be able to read decimal fractions. For example, let's convert 0.3 to an ordinary fraction. 0.3 is zero and three tenths. We write zero integers first:

and next to three tenths 0 . Zero is traditionally not written down, so the final answer will not be 0, but simply.

Example 2 Convert decimal 0.02 to common fraction.

0.02 is zero and two hundredths. We don’t write down zero, so we immediately write down two hundredths

Example 3 Convert 0.00005 to fraction

0.00005 is zero and five hundred thousandths. Zero is not written down, so we immediately write down five hundred thousandths

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