From fraction to decimal online. Convert fraction to decimal online

A fraction is a number that is made up of one or more units. There are three types of fractions in mathematics: common, mixed and decimal.

• 
  Common fractions

An ordinary fraction is written as a ratio in which the numerator reflects how many parts are taken from the number, and the denominator shows how many parts the unit is divided into. If the numerator is less than the denominator, then we have a proper fraction. For example: ½, 3/5, 8/9.

If the numerator is equal to or greater than the denominator, then we are dealing with improper fraction. For example: 5/5, 9/4, 5/2 Dividing the numerator can result in a finite number. For example, 40/8 = 5. Therefore, any whole number can be written as an ordinary improper fraction or a series of such fractions. Let's consider the entries of the same number in the form of a number of different ones.

• Mixed fractions

IN general view a mixed fraction can be represented by the formula:

Thus, a mixed fraction is written as an integer and an ordinary proper fraction, and such a notation is understood as the sum of the whole and its fractional part.

• Decimals

A decimal is a special type of fraction in which the denominator can be represented as a power of 10. There are infinite and finite decimals. When writing this type of fraction, the whole part is first indicated, then the fractional part is recorded through a separator (period or comma).

The notation of a fractional part is always determined by its dimension. The decimal notation looks like this:

Rules for converting between different types of fractions

• Translation mixed fraction to ordinary

A mixed fraction can only be converted to an improper fraction. To translate, it is necessary to bring the whole part to the same denominator as the fractional part. In general it will look like this:
Let's look at the use of this rule using specific examples:

• Converting a common fraction to a mixed fraction

Wrong common fraction can be converted into a mixed one by simple division, which results in the whole part and the remainder (fractional part).

For example, let's convert the fraction 439/31 to mixed:
​​

• Converting fractions

In some cases, converting a fraction to a decimal is quite simple. In this case, the basic property of a fraction is applied: the numerator and denominator are multiplied by the same number in order to bring the divisor to a power of 10.

For example:

In some cases, you may need to find the quotient by dividing by corners or using a calculator. And some fractions cannot be reduced to a final fraction. decimal. For example, the fraction 1/3 when divided will never give the final result.

We have already said that there are fractions ordinary And decimal. On this moment We've studied fractions a little. We learned that there are regular and improper fractions. We also learned that common 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 haven't fully explored common fractions yet. There are many subtleties and details that should be talked about, 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 confusing. It's quite normal. These kinds of lessons require that they be studied, and not skimmed superficially.

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 equal parts, and from these ten parts one part was taken. And one part out of ten in this case is equal to one centimeter:

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

So, you need to show 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, and in centimeters? Fractions come to the rescue. One centimeter is ten millimeters. Three millimeters is three parts out of ten. And three parts out of ten are written as cm

The expression cm means that one centimeter was divided into ten equal parts, and from these ten parts three parts were taken.

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 three centimeters".

Fractions whose denominator contains the numbers 10, 100, 1000 can be written without a denominator. First write the whole 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 it without a denominator. First we write down the whole part. The whole part is 6

The whole part is recorded. Immediately after writing the whole part we 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 a 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 as ordinary 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 mixed number, a decimal fraction 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 a whole part. To write such a fraction as a decimal, first write 0, then put a comma and write the numerator of the fraction. A fraction without a denominator will be written as follows:

Reads like "zero point five".

Converting mixed numbers to decimals

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

After the whole part is written down, it is necessary to count the number of zeros in the denominator of the fractional part, since the number of zeros of 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 definitely need to count the number of zeros in the denominator of the fractional part.

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

Thus, when converted to a decimal fraction, a mixed number becomes 3.2.

This decimal fraction reads like this:

"Three point two"

“Tenths” because the number 10 is in the fractional part of a mixed number.

Example 2. Convert a mixed number to a decimal.

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 the denominator of the fractional part has two zeros. This means that our decimal fraction must have two digits after the decimal point, 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 fraction. Write down the whole part and put a comma:

And write down the numerator of the fractional part:

The decimal fraction 5.03 is read as follows:

"Five point three"

“Hundreds” because the denominator of the fractional part of a mixed number contains the number 100.

Example 3. Convert a mixed number to a decimal.

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

Before converting a mixed number to 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 be the same:

Now you can start converting this mixed number to a decimal fraction. First we write down the whole part 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 fraction 3.002 is read as follows:

"Three point two thousandths"

“Thousandths” because the denominator of the fractional part of the mixed number contains the number 1000.

Converting fractions to decimals

Common fractions with denominators of 10, 100, 1000, or 10000 can also be converted to decimals. 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 also 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 whole part is missing, so first we write 0 and put a comma:

Now we look at the number of zeros in the denominator. We see that there is one zero. And the numerator has one digit. This means 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. This means the fraction is translated correctly.

The decimal fraction 0.5 is read as follows:

"Zero point five"

Example 2. Convert a fraction to a decimal.

A whole part is missing. First we write 0 and put a comma:

Now we 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 fraction:

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. This means the fraction is translated correctly.

The decimal fraction 0.02 is read as follows:

“Zero point two.”

Example 3. Convert a fraction to a decimal.

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 we can continue with the decimal fraction. Write 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. This means the fraction is translated correctly.

The decimal fraction 0.00005 is read as follows:

“Zero point five hundred thousandths.”

Converting improper fractions to decimals

An improper fraction is a fraction in which the numerator is greater than the denominator. There are improper fractions in which the denominator contains the numbers 10, 100, 1000 or 10000. Such fractions can be converted to decimals. But before converting to a decimal fraction, such fractions must be separated into the whole part.

Example 1.

The fraction is an improper fraction. To convert such a fraction to a decimal fraction, you must first select the whole part of it. Let's remember how to isolate the whole part of improper fractions. If you have forgotten, we advise you to return to and study it.

So, let's highlight the whole 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 collect a new mixed number, like children's designer. The number 11 will be the integer part, the number 2 will be the numerator of the fractional part, and the number 10 will be the denominator of the fractional part.

We got a mixed number. Let's convert it to a decimal fraction. And we already know how to convert such numbers into decimal fractions. First, 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 down 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. This means the fraction is translated correctly.

This means that an improper fraction becomes 11.2 when converted to a decimal.

The decimal fraction 11.2 is read as follows:

"Eleven point two."

Example 2. Translate not correct fraction to a decimal fraction.

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

First of all, let's select the whole part of this fraction. To do this, divide 450 by 100 with a corner:

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

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 down 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. This means the fraction is translated correctly.

This means that an improper fraction becomes 4.50 when converted to a decimal.

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

This is one of interesting features decimal fractions. It lies in the fact that the zeros that appear at the end of a 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 does this happen? After all, it looks like 4.50 and 4.5 different fractions. The whole secret lies in the basic property of fractions, 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.”

Converting a decimal to a mixed number

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 point three. First we write down six integers:

and next to three tenths:

Example 2. Convert decimal 3.002 to mixed number

3.002 is three whole and two thousandths. First we write down three integers

and next to it we write two thousandths:

Example 3. Convert decimal 4.50 to mixed number

4.50 is four point fifty. 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 the zero can be discarded. Let's try to prove that the decimals 4.50 and 4.5 are equal. To do this, we convert both decimal fractions into mixed numbers.

When converted to a mixed number, the decimal 4.50 becomes , and the decimal 4.5 becomes

We have two mixed numbers and . Let's convert these mixed numbers to improper fractions:

Now we have two fractions and . It's time to remember the basic property of a fraction, which says that when you multiply (or divide) 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

We got , and this is the second fraction. This means that both are equal to each other and equal to the same value:

Try using a calculator to divide first 450 by 100, and then 45 by 10. It will be a funny thing.

Converting a decimal fraction to a fraction

Any decimal fraction can be converted back to a fraction. To do this, again, it is enough to be able to read decimal fractions. For example, let's convert 0.3 to a common fraction. 0.3 is zero point three. First we write down zero integers:

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 the decimal fraction 0.02 to a fraction.

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

Example 3. Convert 0.00005 to fraction

0.00005 is zero point five. We don’t write down zero, so we immediately write down five hundred thousandths

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It would seem that converting a decimal fraction into a regular fraction is an elementary topic, but many students do not understand it! Therefore, today we will take a detailed look at several algorithms at once, with the help of which you will understand any fractions in just a second.

Let me remind you that there are at least two forms of writing the same fraction: common and decimal. Decimal fractions are all kinds of constructions of the form 0.75; 1.33; and even −7.41. Here are examples of ordinary fractions that express the same numbers:

Now let's figure it out: how to move from decimal notation to regular notation? And most importantly: how to do this as quickly as possible?

Basic algorithm

In fact, there are at least two algorithms. And we'll look at both now. Let's start with the first one - the simplest and most understandable.

To convert a decimal to a fraction, you need to follow three steps:

Important note about negative numbers. If in the original example there is a minus sign in front of the decimal fraction, then in the output there should also be a minus sign in front of the ordinary fraction. Here are some more examples:

I would like to pay special attention to the last example. As you can see, the fraction 0.0025 contains many zeros after the decimal point. Because of this, you have to multiply the numerator and denominator by 10 as many as four times. Is it possible to somehow simplify the algorithm in this case?

Of course you can. And now we will look at an alternative algorithm - it is a little more difficult to understand, but after a little practice it works much faster than the standard one.

Faster way

This algorithm also has 3 steps. To get a fraction from a decimal, do the following:

1. Count how many digits are after the decimal point. For example, the fraction 1.75 has two such digits, and 0.0025 has four. Let's denote this quantity by the letter $n$.
2. Rewrite the original number as a fraction of the form $\frac(a)(((10)^(n)))$, where $a$ are all the digits of the original fraction (without the “starting” zeros on the left, if any), and $n$ is the same number of digits after the decimal point that we calculated in the first step. In other words, you need to divide the digits of the original fraction by one followed by $n$ zeros.
3. If possible, reduce the resulting fraction.

That's all! At first glance, this scheme is more complicated than the previous one. But in fact it is both simpler and faster. Judge for yourself:

As you can see, in the fraction 0.64 there are two digits after the decimal point - 6 and 4. Therefore $n=2$. If we remove the comma and zeros on the left (in this case, just one zero), we get the number 64. Let’s move on to the second step: $((10)^(n))=((10)^(2))=100$, Therefore, the denominator is exactly one hundred. Well, then all that remains is to reduce the numerator and denominator. :)

One more example:

Here everything is a little more complicated. Firstly, there are already 3 numbers after the decimal point, i.e. $n=3$, so you have to divide by $((10)^(n))=((10)^(3))=1000$. Secondly, if we remove the comma from the decimal notation, we get this: 0.004 → 0004. Remember that the zeros on the left must be removed, so in fact we have the number 4. Then everything is simple: divide, reduce and get the answer.

Finally, the last example:

The peculiarity of this fraction is the presence of a whole part. Therefore, the output we get is an improper fraction of 47/25. You can, of course, try to divide 47 by 25 with a remainder and thus again isolate the whole part. But why complicate your life if this can be done at the stage of transformation? Well, let's figure it out.

What to do with the whole part

In fact, everything is very simple: if we want to get a proper fraction, then we need to remove the whole part from it during the transformation, and then, when we get the result, add it again to the right before the fraction line.

For example, consider the same number: 1.88. Let's score by one (the whole part) and look at the fraction 0.88. It can be easily converted:

Then we remember about the “lost” unit and add it to the front:

\[\frac(22)(25)\to 1\frac(22)(25)\]

That's all! The answer turned out to be the same as after selecting the whole part last time. A couple more examples:

\[\begin(align)& 2.15\to 0.15=\frac(15)(100)=\frac(3)(20)\to 2\frac(3)(20); \\& 13.8\to 0.8=\frac(8)(10)=\frac(4)(5)\to 13\frac(4)(5). \\\end(align)\]

This is the beauty of mathematics: no matter which way you go, if all the calculations are done correctly, the answer will always be the same. :)

In conclusion, I would like to consider one more technique that helps many.

Transformations “by ear”

Let's think about what a decimal fraction is. More precisely, how we read it. For example, the number 0.64 - we read it as "zero point 64 hundredths", right? Well, or just “64 hundredths”. The key word here is “hundredths”, i.e. number 100.

What about 0.004? This is “zero point 4 thousandths” or simply “four thousandths”. One way or another, the key word is “thousands”, i.e. 1000.

So what's the big deal? And the fact is that it is these numbers that ultimately “pop up” in the denominators at the second stage of the algorithm. Those. 0.004 is “four thousandths” or “4 divided by 1000”:

Try to practice yourself - it's very simple. The main thing is to read the original fraction correctly. For example, 2.5 is “2 whole, 5 tenths”, so

And some 1.125 is “1 whole, 125 thousandths”, so

In the last example, of course, someone will object that it is not obvious to every student that 1000 is divisible by 125. But here you need to remember that 1000 = 10 3, and 10 = 2 ∙ 5, therefore

\[\begin(align)& 1000=10\cdot 10\cdot 10=2\cdot 5\cdot 2\cdot 5\cdot 2\cdot 5= \\& =2\cdot 2\cdot 2\cdot 5\ cdot 5\cdot 5=8\cdot 125\end(align)\]

Thus, any power of ten can be decomposed only into factors 2 and 5 - it is these factors that need to be looked for in the numerator so that in the end everything is reduced.

This concludes the lesson. Let's move on to a more complex reverse operation - see "

Converting a Fraction to a Decimal

Let's say we want to convert the fraction 11/4 to a decimal. The easiest way to do it is this:

We succeeded because in this case the decomposition of the denominator into prime factors consists only of twos. We supplemented this expansion with two more fives, took advantage of the fact that 10 = 2∙5, and got a decimal fraction. Such a procedure is obviously possible if and only if the decomposition of the denominator into prime factors contains nothing but twos and fives. If any other prime number is present in the expansion of the denominator, then such a fraction cannot be converted to a decimal. Nevertheless, we will try to do this, but only in a different way, which we will get acquainted with using the example of the same fraction 11/4. Let's divide 11 by 4 using the “corner”:

In the response line we received the whole part (2), and we also have the remainder (3). Previously, we ended the division here, but now we know that we can add a comma and several zeros to the right of the dividend (11), which we will now mentally do. After the decimal point comes the tenths place. The zero that appears at the dividend in this digit will be added to the resulting remainder (3):

Now the division can continue as if nothing had happened. You just need to remember to put a comma after the whole part in the answer line:

Now we add a zero to the remainder (2), which is in the hundredths place of the dividend, and complete the division:

As a result, we get, as before,

Let's now try to calculate in exactly the same way what the fraction 27/11 is equal to:

We received the number 2.45 in the answer line, and the number 5 in the remainder line. But we have already encountered such a remnant before. Therefore, we can immediately say that if we continue our division with a “corner”, then the next number in the answer line will be 4, then the number 5 will come, then again 4 and again 5, and so on, ad infinitum:

27 / 11 = 2,454545454545...

We got the so-called periodic a decimal fraction with a period of 45. For such fractions, a more compact notation is used, in which the period is written only once, but it is enclosed in parentheses:

2,454545454545... = 2,(45).

Generally speaking, if you divide one thing into a “corner” natural number on the other hand, writing the answer in the form of a decimal fraction, then only two outcomes are possible: (1) either sooner or later we will get zero in the remainder line, (2) or there will be a remainder that we have already encountered before (the set of possible remainders is limited, because they all obviously less than divisor). In the first case, the result of division is a finite decimal fraction, in the second case - a periodic one.

Convert periodic decimal to fraction

Let us be given a positive periodic decimal fraction with a zero integer part, for example:

a = 0,2(45).

How can I convert this fraction back to a common fraction?

Let's multiply it by 10 k, Where k is the number of digits between the decimal point and the opening parenthesis indicating the beginning of the period. In this case k= 1 and 10 k = 10:

a∙ 10 k = 2,(45).

Multiply the result by 10 n, Where n- the “length” of the period, that is, the number of digits enclosed between parentheses. In this case n= 2 and 10 n = 100:

a∙ 10 k ∙ 10 n = 245,(45).

Now let's calculate the difference

a∙ 10 k ∙ 10 n − a∙ 10 k = 245,(45) − 2,(45).

Since the fractional parts of the minuend and the subtrahend are the same, then the fractional part of the difference is equal to zero, and we come to simple equation relatively a:

a∙ 10 k ∙ (10 n − 1) = 245 − 2.

This equation is solved using the following transformations:

a∙ 10 ∙ (100 − 1) = 245 − 2.

a∙ 10 ∙ 99 = 245 − 2.

We deliberately do not complete the calculations yet, so that it is clearly visible how this result can be immediately written down, omitting intermediate arguments. The minuend in the numerator (245) is the fractional part of the number

a = 0,2(45)

if you erase the brackets in her entry. The subtrahend in the numerator (2) is the non-periodic part of the number A, located between the comma and the opening parenthesis. The first factor in the denominator (10) is a unit, to which as many zeros are assigned as there are digits in the non-periodic part ( k). The second factor in the denominator (99) is as many nines as there are digits in the period ( n).

Now our calculations can be completed:

Here the numerator contains the period, and the denominator contains as many nines as there are digits in the period. After reduction by 9, the resulting fraction is equal to

In the same way,

Materials on fractions and study sequentially. Below you will find detailed information with examples and explanations.

1. Mixed number into a common fraction.Let's write the number in general form:

We remember a simple rule - we multiply the whole part by the denominator and add the numerator, that is:

Examples:

2. On the contrary, an ordinary fraction into a mixed number. *Of course, this can only be done with an improper fraction (when the numerator is greater than the denominator).

With “small” numbers, in general, no actions need to be taken; the result is “visible” immediately, for example, fractions:

*More details:

15:13 = 1 remainder 2

4:3 = 1 remainder 1

9:5 = 1 remainder 4

But if the numbers are more, then you can’t do without calculations. Everything is simple here - divide the numerator by the denominator with a corner until the remainder is less than the divisor. Division scheme:

For example:

*Our numerator is the dividend, the denominator is the divisor.

We get the whole part (incomplete quotient) and the remainder. We write down an integer, then a fraction (the numerator contains the remainder, but the denominator remains the same):

3. Convert decimal to ordinary.

Partially in the first paragraph, where we talked about decimal fractions, we already touched on this. We write it down as we hear it. For example - 0.3; 0.45; 0.008; 4.38; 10.00015

We have the first three fractions without an integer part. And the fourth and fifth ones have it, let’s convert them into ordinary ones, we already know how to do this:

*We see that fractions can also be reduced, for example 45/100 = 9/20, 38/100 = 19/50 and others, but we will not do this here. Regarding reduction, you will find a separate paragraph below, where we will analyze everything in detail.

4. Convert ordinary to decimal.

It's not that simple. With some fractions it is immediately obvious and clear what to do with it so that it becomes a decimal, for example:

We use our wonderful basic property of a fraction - we multiply the numerator and denominator by 5, 25, 2, 5, 4, 2, respectively, and we get:

If there is an entire part, then it’s also not complicated:

We multiply the fractional part by 2, 25, 2 and 5, respectively, and get:

And there are those for which without experience it is impossible to determine that they can be converted into decimals, for example:

What numbers should we multiply the numerator and denominator by?

Here again a proven method comes to the rescue - division by a corner, a universal method, you can always use it to convert a common fraction to a decimal:

This way you can always determine whether a fraction is converted to a decimal. The fact is that not every ordinary fraction can be converted to a decimal, for example, such as 1/9, 3/7, 7/26 are not converted. What then is the fraction obtained when dividing 1 by 9, 3 by 7, 5 by 11? My answer is infinite decimal (we talked about them in paragraph 1). Let's divide:

That's all! Good luck to you!

Sincerely, Alexander Krutitskikh.