It happens that for the convenience of calculations you need to convert an ordinary fraction to a decimal and vice versa. We will talk about how to do this in this article. Let's look at the rules for converting ordinary fractions to decimals and vice versa, and also give examples.
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We will consider converting ordinary fractions to decimals, following a certain sequence. First, let's look at how ordinary fractions with a denominator that is a multiple of 10 are converted into decimals: 10, 100, 1000, etc. Fractions with such denominators are, in fact, a more cumbersome notation of decimal fractions.
Next, we will look at how to convert ordinary fractions with any denominator, not just multiples of 10, into decimal fractions. Note that when converting ordinary fractions to decimals, not only finite decimals are obtained, but also infinite periodic decimal fractions.
Let's get started!
Translation of ordinary fractions with denominators 10, 100, 1000, etc. to decimals
First of all, let's say that some fractions require some preparation before converting to decimal form. What is it? Before the number in the numerator, you need to add so many zeros so that the number of digits in the numerator becomes equal to the number of zeros in the denominator. For example, for the fraction 3100, the number 0 must be added once to the left of the 3 in the numerator. Fraction 610, according to the rule stated above, does not need modification.
Let's look at one more example, after which we will formulate a rule that is especially convenient to use at first, while there is not much experience in converting fractions. So, the fraction 1610000 after adding zeros in the numerator will look like 001510000.
How to convert a common fraction with a denominator of 10, 100, 1000, etc. to decimal?
Rule for converting ordinary proper fractions to decimals
- Write down 0 and put a comma after it.
- We write down the number from the numerator that was obtained after adding zeros.
Now let's move on to examples.
Example 1: Converting fractions to decimals
Let's convert the fraction 39,100 to a decimal.
First, we look at the fraction and see that there is no need to carry out any preparatory actions - the number of digits in the numerator coincides with the number of zeros in the denominator.
Following the rule, we write 0, put a decimal point after it and write the number from the numerator. We get the decimal fraction 0.39.
Let's look at the solution to another example on this topic.
Example 2. Converting fractions to decimals
Let's write the fraction 105 10000000 as a decimal.
The number of zeros in the denominator is 7, and the numerator has only three digits. Let's add 4 more zeros before the number in the numerator:
0000105 10000000
Now we write down 0, put a decimal point after it and write down the number from the numerator. We get the decimal fraction 0.0000105.
The fractions considered in all examples are ordinary proper fractions. But how do you convert an improper fraction to a decimal? Let’s say right away that there is no need for preparation with adding zeros for such fractions. Let's formulate a rule.
Rule for converting ordinary improper fractions to decimals
- Write down the number that is in the numerator.
- We use a decimal point to separate as many digits on the right as there are zeros in the denominator of the original fraction.
Below is an example of how to use this rule.
Example 3. Converting fractions to decimals
Let's convert the fraction 56888038009 100000 from an ordinary irregular fraction to a decimal.
First, let's write down the number from the numerator:
Now, on the right, we separate five digits with a decimal point (the number of zeros in the denominator is five). We get:
The next question that naturally arises is: how to convert a mixed number into a decimal fraction if the denominator of its fractional part is the number 10, 100, 1000, etc. To convert such a number to a decimal fraction, you can use the following rule.
Rule for converting mixed numbers to decimals
- We prepare the fractional part of the number, if necessary.
- We write down the whole part of the original number and put a comma after it.
- We write down the number from the numerator of the fractional part along with the added zeros.
Let's look at an example.
Example 4: Converting mixed numbers to decimals
Let's convert the mixed number 23 17 10000 to a decimal fraction.
In the fractional part we have the expression 17 10000. Let's prepare it and add two more zeros to the left of the numerator. We get: 0017 10000.
Now we write down the whole part of the number and put a comma after it: 23, . .
After the decimal point, write down the number from the numerator along with zeros. We get the result:
23 17 10000 = 23 , 0017
Converting ordinary fractions to finite and infinite periodic fractions
Of course, you can convert to decimals and ordinary fractions with a denominator not equal to 10, 100, 1000, etc.
Often a fraction can be easily reduced to a new denominator, and then use the rule set out in the first paragraph of this article. For example, it is enough to multiply the numerator and denominator of the fraction 25 by 2, and we get the fraction 410, which is easily converted to the decimal form 0.4.
However, this method of converting a fraction to a decimal cannot always be used. Below we will consider what to do if it is impossible to apply the considered method.
A fundamentally new way to convert a fraction to a decimal is to divide the numerator by the denominator with a column. This operation is very similar to dividing natural numbers with a column, but has its own characteristics.
When dividing, the numerator is represented as a decimal fraction - a comma is placed to the right of the last digit of the numerator and zeros are added. In the resulting quotient, a decimal point is placed when the division of the integer part of the numerator ends. How exactly this method works will become clear after looking at the examples.
Example 5. Converting fractions to decimals
Let's convert the common fraction 621 4 to decimal form.
Let's represent the number 621 from the numerator as a decimal fraction, adding a few zeros after the decimal point. 621 = 621.00
Now let's divide 621.00 by 4 using a column. The first three steps of division will be the same as when dividing natural numbers, and we will get.
When we reach the decimal point in the dividend, and the remainder is different from zero, we put a decimal point in the quotient and continue dividing, no longer paying attention to the comma in the dividend.
As a result, we get the decimal fraction 155, 25, which is the result of reversing the common fraction 621 4
621 4 = 155 , 25
Let's look at another example to reinforce the material.
Example 6. Converting fractions to decimals
Let's reverse the common fraction 21 800.
To do this, divide the fraction 21,000 into a column by 800. The division of the whole part will end at the first step, so immediately after it we put a decimal point in the quotient and continue the division, not paying attention to the comma in the dividend until we get a remainder equal to zero.
As a result, we got: 21,800 = 0.02625.
But what if, when dividing, we still do not get a remainder of 0. In such cases, the division can be continued indefinitely. However, starting from a certain step, the residues will be repeated periodically. Accordingly, the numbers in the quotient will be repeated. This means that an ordinary fraction is converted into a decimal infinite periodic fraction. Let us illustrate this with an example.
Example 7. Converting fractions to decimals
Let's convert the common fraction 19 44 to a decimal. To do this, we perform division by column.
We see that during division, residues 8 and 36 are repeated. In this case, the numbers 1 and 8 are repeated in the quotient. This is the period in decimal fraction. When recording, these numbers are placed in brackets.
Thus, the original ordinary fraction is converted into an infinite periodic decimal fraction.
19 44 = 0 , 43 (18) .
Let us see an irreducible ordinary fraction. What form will it take? Which ordinary fractions are converted to finite decimals, and which ones are converted to infinite periodic ones?
First, let's say that if a fraction can be reduced to one of the denominators 10, 100, 1000..., then it will have the form of a final decimal fraction. In order for a fraction to be reduced to one of these denominators, its denominator must be a divisor of at least one of the numbers 10, 100, 1000, etc. From the rules for factoring numbers into prime factors it follows that the divisor of numbers is 10, 100, 1000, etc. must, when factored into prime factors, contain only the numbers 2 and 5.
Let's summarize what has been said:
- A common fraction can be reduced to a final decimal if its denominator can be factored into prime factors of 2 and 5.
- If, in addition to the numbers 2 and 5, there are other prime numbers in the expansion of the denominator, the fraction is reduced to the form of an infinite periodic decimal fraction.
Let's give an example.
Example 8. Converting fractions to decimals
Which of these fractions 47 20, 7 12, 21 56, 31 17 is converted into a final decimal fraction, and which one - only into a periodic one. Let's answer this question without directly converting a fraction to a decimal.
The fraction 47 20, as is easy to see, by multiplying the numerator and denominator by 5 is reduced to a new denominator 100.
47 20 = 235 100. From this we conclude that this fraction is converted to a final decimal fraction.
Factoring the denominator of the fraction 7 12 gives 12 = 2 · 2 · 3. Since the prime factor 3 is different from 2 and 5, this fraction cannot be represented as a finite decimal fraction, but will have the form of an infinite periodic fraction.
The fraction 21 56, firstly, needs to be reduced. After reduction by 7, we obtain the irreducible fraction 3 8, the denominator of which is factorized to give 8 = 2 · 2 · 2. Therefore, it is a final decimal fraction.
In the case of the fraction 31 17, factoring the denominator is the prime number 17 itself. Accordingly, this fraction can be converted into an infinite periodic decimal fraction.
An ordinary fraction cannot be converted into an infinite and non-periodic decimal fraction
Above we talked only about finite and infinite periodic fractions. But can any ordinary fraction be converted into an infinite non-periodic fraction?
We answer: no!
Important!
When converting an infinite fraction to a decimal, the result is either a finite decimal or an infinite periodic decimal.
The remainder of a division is always less than the divisor. In other words, according to the divisibility theorem, if we divide some natural number by the number q, then the remainder of the division in any case cannot be greater than q-1. After the division is completed, one of the following situations is possible:
- We get a remainder of 0, and this is where the division ends.
- We get a remainder, which is repeated upon subsequent division, resulting in an infinite periodic fraction.
There cannot be any other options when converting a fraction to a decimal. Let's also say that the length of the period (number of digits) in an infinite periodic fraction is always less than the number of digits in the denominator of the corresponding ordinary fraction.
Converting decimals to fractions
Now it's time to look at the reverse process of converting a decimal fraction into a common fraction. Let us formulate a translation rule that includes three stages. How to convert a decimal fraction to a common fraction?
Rule for converting decimal fractions to ordinary fractions
- In the numerator we write the number from the original decimal fraction, discarding the comma and all zeros on the left, if any.
- In the denominator we write one followed by as many zeros as there are digits after the decimal point in the original decimal fraction.
- If necessary, reduce the resulting ordinary fraction.
Let's look at the application of this rule using examples.
Example 8. Converting decimal fractions to ordinary fractions
Let's imagine the number 3.025 as an ordinary fraction.
- We write the decimal fraction itself into the numerator, discarding the comma: 3025.
- In the denominator we write one, and after it three zeros - this is exactly how many digits are contained in the original fraction after the decimal point: 3025 1000.
- The resulting fraction 3025 1000 can be reduced by 25, resulting in: 3025 1000 = 121 40.
Example 9. Converting decimal fractions to ordinary fractions
Let's convert the fraction 0.0017 from decimal to ordinary.
- In the numerator we write the fraction 0, 0017, discarding the comma and zeros on the left. It will turn out to be 17.
- We write one in the denominator, and after it we write four zeros: 17 10000. This fraction is irreducible.
If a decimal fraction has an integer part, then such a fraction can be immediately converted to a mixed number. How to do it?
Let's formulate one more rule.
Rule for converting decimals to mixed numbers.
- The number before the decimal point in the fraction is written as the integer part of the mixed number.
- In the numerator we write the number after the decimal point in the fraction, discarding the zeros on the left if there are any.
- In the denominator of the fractional part we add one and as many zeros as there are digits after the decimal point in the fractional part.
Let's take an example
Example 10. Converting a decimal to a mixed number
Let's imagine the fraction 155, 06005 as a mixed number.
- We write the number 155 as an integer part.
- In the numerator we write the numbers after the decimal point, discarding the zero.
- We write one and five zeros in the denominator
Let's learn a mixed number: 155 6005 100000
The fractional part can be reduced by 5. We shorten it and get the final result:
155 , 06005 = 155 1201 20000
Converting infinite periodic decimals to fractions
Let's look at examples of how to convert periodic decimal fractions into ordinary fractions. Before we begin, let's clarify: any periodic decimal fraction can be converted to an ordinary fraction.
The simplest case is when the period of the fraction is zero. A periodic fraction with a zero period is replaced by a final decimal fraction, and the process of reversing such a fraction is reduced to reversing the final decimal fraction.
Example 11. Converting a periodic decimal fraction to a common fraction
Let us invert the periodic fraction 3, 75 (0).
Eliminating the zeros on the right, we get the final decimal fraction 3.75.
Converting this fraction to an ordinary fraction using the algorithm discussed in the previous paragraphs, we obtain:
3 , 75 (0) = 3 , 75 = 375 100 = 15 4 .
What if the period of the fraction is different from zero? The periodic part should be considered as the sum of the terms of a geometric progression, which decreases. Let's explain this with an example:
0 , (74) = 0 , 74 + 0 , 0074 + 0 , 000074 + 0 , 00000074 + . .
There is a formula for the sum of terms of an infinite decreasing geometric progression. If the first term of the progression is b and the denominator q is such that 0< q < 1 , то сумма равна b 1 - q .
Let's look at a few examples using this formula.
Example 12. Converting a periodic decimal fraction to a common fraction
Let us have a periodic fraction 0, (8) and we need to convert it to an ordinary one.
0 , (8) = 0 , 8 + 0 , 08 + 0 , 008 + . .
Here we have an infinite decreasing geometric progression with the first term 0, 8 and the denominator 0, 1.
Let's apply the formula:
0 , (8) = 0 , 8 + 0 , 08 + 0 , 008 + . . = 0 , 8 1 - 0 , 1 = 0 , 8 0 , 9 = 8 9
This is the required ordinary fraction.
To consolidate the material, consider another example.
Example 13. Converting a periodic decimal fraction to a common fraction
Let's reverse the fraction 0, 43 (18).
First we write the fraction as an infinite sum:
0 , 43 (18) = 0 , 43 + (0 , 0018 + 0 , 000018 + 0 , 00000018 . .)
Let's look at the terms in brackets. This geometric progression can be represented as follows:
0 , 0018 + 0 , 000018 + 0 , 00000018 . . = 0 , 0018 1 - 0 , 01 = 0 , 0018 0 , 99 = 18 9900 .
We add the result to the final fraction 0, 43 = 43 100 and get the result:
0 , 43 (18) = 43 100 + 18 9900
After adding these fractions and reducing, we get the final answer:
0 , 43 (18) = 19 44
To conclude this article, we will say that non-periodic infinite decimal fractions cannot be converted into ordinary fractions.
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At the very beginning, you still need to find out what a fraction is and what types it comes in. And there are three types. And the first of them is an ordinary fraction, for example ½, 3/7, 3/432, etc. These numbers can also be written using a horizontal dash. Both the first and second will be equally true. The number on top is called the numeral, and the number on the bottom is called the denominator. There is even a saying for those people who constantly confuse these two names. It goes like this: “Zzzzz remember! Zzzz denominator - downzzzz! " This will help you avoid getting confused. A common fraction is just two numbers that are divisible by each other. The dash in them indicates the division sign. It can be replaced with a colon. If the question is “how to convert a fraction into a number,” then it is very simple. You just need to divide the numerator by the denominator. That's all. The fraction has been translated.
The second type of fraction is called decimal. This is a series of numbers followed by a comma. For example, 0.5, 3.5, etc. They were called decimal only because after the sung number the first digit means “tens”, the second is ten times more than “hundreds”, and so on. And the first digits before the decimal point are called integers. For example, the number 2.4 sounds like this, twelve point two and two hundred thirty-four thousandths. Such fractions appear mainly due to the fact that dividing two numbers without a remainder does not work. And most fractions, when converted to numbers, end up as decimals. For example, one second is equal to zero point five.
And the final third view. These are mixed numbers. An example of this can be given as 2½. It sounds like two wholes and one second. In high school, this type of fractions is no longer used. They will probably need to be converted either to ordinary fraction form or to decimal form. It's just as easy to do this. You just need to multiply the integer by the denominator and add the resulting notation to the numeral. Let's take our example 2½. Two multiplied by two equals four. Four plus one equals five. And a fraction of the shape 2½ is formed into 5/2. And five, divided by two, can be obtained as a decimal fraction. 2½=5/2=2.5. It has already become clear how to convert fractions into numbers. You just need to divide the numerator by the denominator. If the numbers are large, you can use a calculator.
If it does not produce whole numbers and there are a lot of digits after the decimal point, then this value can be rounded. Everything is rounded up very simply. First you need to decide what number you need to round to. An example should be considered. A person needs to round the number zero point zero, nine thousand seven hundred fifty-six ten thousandths, or to the digital value of 0.6. Rounding must be done to the nearest hundredth. This means that at the moment it is up to seven hundredths. After the number seven in the fraction there is five. Now we need to use the rules for rounding. Numbers greater than five are rounded up, and numbers smaller than five are rounded down. In the example, the person has five, she is on the border, but it is considered that rounding occurs upward. This means that we remove all the numbers after seven and add one to it. It turns out 0.8.
Situations also arise when a person needs to quickly convert a common fraction into a number, but there is no calculator nearby. To do this, use column division. The first step is to write the numerator and denominator next to each other on a piece of paper. A dividing corner is placed between them; it looks like the letter “T”, only lying on its side. For example, you can take the fraction ten sixths. And so, ten should be divided by six. How many sixes can fit in a ten, only one. The unit is written under the corner. Ten subtract six equals four. How many sixes will there be in a four, several. This means that in the answer a comma is placed after the one, and the four is multiplied by ten. At forty-six sixes. Six is added to the answer, and thirty-six is subtracted from forty. That turns out to be four again.
In this example, a loop has occurred, if you continue to do everything exactly the same, you will get the answer 1.6(6). The number six continues to infinity, but by applying the rounding rule, you can bring the number to 1.7. Which is much more convenient. From this we can conclude that not all ordinary fractions can be converted to decimals. In some there is a cycle. But any decimal fraction can be converted into a simple fraction. An elementary rule will help here: as it is heard, so it is written. For example, the number 1.5 is heard as one point twenty-five hundredths. So you need to write it down, one whole, twenty-five divided by one hundred. One whole number is one hundred, which means that the simple fraction will be one hundred and twenty-five times one hundred (125/100). Everything is also simple and clear.
So the most basic rules and transformations that are associated with fractions have been discussed. They are all simple, but you should know them. Fractions, especially decimals, have long been part of everyday life. This is clearly visible on price tags in stores. It’s been a long time since anyone writes round prices, but with fractions the price seems visually much cheaper. Also, one of the theories says that humanity turned away from Roman numerals and adopted Arabic ones, only because Roman ones did not have fractions. And many scientists agree with this assumption. After all, with fractions you can make calculations more accurately. And in our age of space technology, accuracy in calculations is needed more than ever. So studying fractions in school mathematics is vital for understanding many sciences and technological advances.
A large number of students, and not only, are wondering how to convert a fraction into a number. To do this, there are several fairly simple and understandable ways. The choice of a specific method depends on the preferences of the decider.
First of all, you need to know how fractions are written. And they are written as follows:
- Ordinary. It is written with the numerator and denominator using a slant or a column (1/2).
- Decimal. It is written separated by commas (1.0, 2.5, and so on).
Before you start solving, you need to know what an improper fraction is, because it occurs quite often. It has a numerator greater than the denominator, for example, 15/6. Improper fractions can also be solved in these ways, without any effort or time.
A mixed number is when the result is a whole number and a fractional part, for example 52/3.
Any natural number can be written as a fraction with completely different natural denominators, for example: 1= 2/2=3/3 = etc.
You can also translate using a calculator, but not all of them have this function. There is a special engineering calculator that has such a function, but it is not always possible to use it, especially at school. Therefore, it is better to understand this topic.
The first thing you should pay attention to is what fraction it is. If it can be easily multiplied up to 10 by the same values as the numerator, then you can use the first method. For example: you multiply an ordinary ½ in the numerator and denominator by 5 and get 5/10, which can be written as 0.5.
This rule is based on the fact that a decimal always has a round value in its denominator, such as 10,100,1000, and so on.
It follows from this that if you multiply the numerator and the denominator, then you need to achieve exactly the same value in the denominator as a result of the multiplication, regardless of what comes out in the numerator.
It is worth remembering that some fractions cannot be converted; to do this, you need to check it before starting the solution.
For example: 1.3333, where the number 3 is repeated ad infinitum, and the calculator will not get rid of it either. The only solution to this problem is to round it to a whole number, if possible. If this is not possible, then you should return to the beginning of the example and check the correctness of the solution to the problem; perhaps an error was made.
Figure 1-3. Converting fractions by multiplication.
To consolidate the described information, consider the following translation example:
- For example, you need to convert 6/20 to a decimal. The first step is to check it, as shown in Figure 1.
- Only after you are convinced that it can be decomposed, as in this case into 2 and 5, should you begin the translation itself.
- The simplest option would be to multiply the denominator to get a result of 100, which is 5, since 20x5=100.
- Following the example in Figure 2, the result will be 0.3.
You can consolidate the result and review everything again according to Figure 3. In order to fully understand the topic and no longer resort to studying this material. This knowledge will help not only the child, but also the adult.
Translation by division
The second option for converting fractions is a little more complicated, but more popular. This method is mainly used by teachers in schools to explain. Overall, it is much easier to explain and quicker to understand.
It is worth remembering that to correctly convert a simple fraction, you must divide its numerator by its denominator. After all, if you think about it, the solution is the process of division.
In order to understand this simple rule, you need to consider the following example solution:
- Let's take 78/200, which needs to be converted to decimal. To do this, divide 78 by 200, that is, the numerator by the denominator.
- But before you start, it's worth checking, as shown in Figure 4.
- Once you are convinced that it can be solved, you should begin the process. To do this, it is worth dividing the numerator by the denominator in a column or corner, as shown in Figure 5. In primary schools, such division is taught, and there should be no difficulties with this.
Figure 6 shows examples of the most common examples; you can simply remember them so that, if necessary, you do not waste time solving them. After all, at school, each test or independent work is given little time to solve, so you shouldn’t waste it on something that you can learn and simply remember.
Interest transfer
Converting percentages to decimals is also quite easy. This begins to be taught in the 5th grade, and in some schools even earlier. But if your child did not understand this topic during a math lesson, you can clearly explain it to him again. First, you should learn the definition of what a percentage is.
A percentage is one hundredth of a number; in other words, it is completely arbitrary. For example, from 100 it will be 1 and so on.
Figure 7 shows a clear example of interest conversion.
To convert a percentage, you just need to remove the % sign and then divide it by 100.
Another example is shown in Figure 8.
If you need to carry out a reverse “conversion”, you need to do everything exactly the opposite. In other words, the number must be multiplied by one hundred and then a percentage symbol must be added.
And in order to convert the usual into percentages, you can also use this example. Only initially should you convert the fraction into a number and only then into a percentage.
Based on the above, you can easily understand the principle of translation. Using these methods, you can explain a topic to a child if he did not understand it or was not present in the lesson at the time of its completion.
And there will never be a need to hire a tutor to explain to your child how to convert a fraction into a number or percentage.
A fraction can be converted to a whole number or to a decimal. An improper fraction, the numerator of which is greater than the denominator and is divisible by it without a remainder, is converted to a whole number, for example: 20/5. Divide 20 by 5 and get the number 4. If the fraction is proper, that is, the numerator is less than the denominator, then convert it to a number (decimal fraction). You can get more information about fractions from our section -.
Ways to convert a fraction to a number
- The first way to convert a fraction into a number is suitable for a fraction that can be converted to a number that is a decimal fraction. First, let's find out whether it is possible to convert the given fraction to a decimal fraction. To do this, let's pay attention to the denominator (the number that is below the line or to the right of the sloping line). If the denominator can be factorized (in our example - 2 and 5), which can be repeated, then this fraction can actually be converted into a final decimal fraction. For example: 11/40 =11/(2∙2∙2∙5). This common fraction will be converted to a number (decimal) with a finite number of decimal places. But the fraction 17/60 =17/(5∙2∙2∙3) will be converted into a number with an infinite number of decimal places. That is, when accurately calculating a numerical value, it is quite difficult to determine the final decimal place, since there are an infinite number of such signs. Therefore, solving problems usually requires rounding the value to hundredths or thousandths. Next, you need to multiply both the numerator and the denominator by such a number so that the denominator produces the numbers 10, 100, 1000, etc. For example: 11/40 =(11∙25)/(40∙25) =275/1000 = 0.275
- The second way to convert a fraction into a number is simpler: you need to divide the numerator by the denominator. To apply this method, we simply perform division, and the resulting number will be the desired decimal fraction. For example, you need to convert the fraction 2/15 into a number. Divide 2 by 15. We get 0.1333... - an infinite fraction. We write it like this: 0.13(3). If the fraction is an improper fraction, that is, the numerator is greater than the denominator (for example, 345/100), then converting it to a number will result in a whole number value or a decimal fraction with a whole fractional part. In our example it will be 3.45. To convert a mixed fraction like 3 2 / 7 into a number, you must first convert it to an improper fraction: (3∙7+2)/7 = 23/7. Next, divide 23 by 7 and get the number 3.2857143, which we reduce to 3.29.
The easiest way to convert a fraction into a number is to use a calculator or other computing device. First we indicate the numerator of the fraction, then press the button with the “divide” icon and enter the denominator. After pressing the "=" key, we get the desired number.
Decimal numbers such as 0.2; 1.05; 3.017, etc. as they are heard, so they are written. Zero point two, we get a fraction. One point five hundredths, we get a fraction. Three point seventeen thousandths, we get the fraction. The numbers before the decimal point are the whole part of the fraction. The number after the decimal point is the numerator of the future fraction. If there is a single-digit number after the decimal point, the denominator will be 10, if there is a two-digit number - 100, a three-digit number - 1000, etc. Some resulting fractions can be reduced. In our examples 
Converting a fraction to a decimal
This is the reverse of the previous transformation. What is the characteristic of a decimal fraction? Its denominator is always 10, or 100, or 1000, or 10000, and so on. If your common fraction has a denominator like this, there's no problem. For example, or
If the fraction is, for example . In this case, it is necessary to use the basic property of a fraction and convert the denominator to 10 or 100, or 1000... In our example, if we multiply the numerator and denominator by 4, we get a fraction that can be written as a decimal number 0.12.
Some fractions are easier to divide than to convert the denominator. For example,
Some fractions cannot be converted to decimals!
For example,
Converting a mixed fraction to an improper fraction
A mixed fraction, for example, can be easily converted to an improper fraction. To do this, you need to multiply the whole part by the denominator (bottom) and add it with the numerator (top), leaving the denominator (bottom) unchanged. That is
When converting a mixed fraction to an improper fraction, you can remember that you can use fraction addition
Converting an improper fraction to a mixed fraction (highlighting the whole part)
An improper fraction can be converted to a mixed fraction by highlighting the whole part. Let's look at an example. We determine how many integer times “3” fits into “23”. Or divide 23 by 3 on a calculator, the whole number to the decimal point is the desired one. This is "7". Next, we determine the numerator of the future fraction: we multiply the resulting “7” by the denominator “3” and subtract the result from the numerator “23”. 
It’s as if we find the extra that remains from the numerator “23” if we remove the maximum amount of “3”. We leave the denominator unchanged. Everything is done, write down the result
