Converting a fraction to a decimal

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

						2∙2∙5∙5

We succeeded because in this case the factorization 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 factorization 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 on the example of the same fraction 11/4. Let's divide 11 by 4 "corner":

In the response line, we got the integer part ( 2 ), and we also have the remainder ( 3 ). Previously, we ended the division on this, but now we know that a comma and a few zeros can be attributed to the dividend ( 11 ) on the right, which we will mentally do now. After the decimal point comes the tenth place. Zero, which stands for the dividend in this category, we will attribute 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 integer part in the answer line:

Now we attribute to the remainder ( 2 ) zero, which stands for the dividend in the hundredths place and bring the division to the end:

As a result, we get, as before,

Now let's 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 seen such a remnant before. Therefore, we can immediately say that if we continue our division by the “corner”, then the next digit in the answer line will be 4, then the number 5 will go, then again 4 and again 5, and so on, ad infinitum:

27 / 11 = 2,454545454545...

We have received the so-called periodical a decimal fraction with a period of 45. For such fractions, a more compact notation is used, in which the period is written out only once, but at the same time it is enclosed in parentheses:

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

Generally speaking, if we divide one natural number by a “corner” by another, writing the answer as 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 such a remainder, which we have already encountered before (the set of possible residues is limited, since they are all obviously less than the divisor). In the first case, the result of division is a final decimal fraction, in the second case, a periodic one.

Converting a Periodic Decimal to a Common 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 comma and the opening parenthesis that indicates 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- "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 zero, and we arrive at a simple equation for 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.

	245 − 2
	10 ∙ 99

We deliberately do not bring the calculations to the end yet, so that it can be clearly seen how this result can be written out immediately, omitting intermediate arguments. Decreasing in the numerator ( 245 ) is the fractional part of the number

a = 0,2(45)

if you delete the brackets in her entry. The subtrahend in the numerator ( 2 ) is the non-periodic part of the number but, located between the comma and the opening parenthesis. The first factor in the denominator ( 10 ) is one, 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 there is a period in the numerator, and as many nines in the denominator as there are digits in the period. After reducing by 9, the resulting fraction is equal to

In the same way,

A fraction is a number that consists of one or more fractions of a unit. 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 of the number are taken, 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 an improper fraction. For example: 5/5, 9/4, 5/2 Dividing the numerator can result in a finite number. For example, 40/8 \u003d 5. Therefore, any integer can be written as an ordinary improper fraction or a series of such fractions. Consider writing the same number as a series of different .

• mixed fractions

In general, 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 record is understood as the sum of a whole and its fractional part.

• Decimals

A decimal is a special kind 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 integer part is first indicated, then the fractional part is fixed through the separator (dot or comma).

The record of the fractional part is always determined by its dimension. The decimal entry looks like this:

Translation rules between different types of fractions

• Converting a mixed fraction to a common fraction

A mixed fraction can only be converted to an improper fraction. For translation, it is necessary to bring the whole part to the same denominator as the fractional part. In general, it will look like this:
Consider the use of this rule on specific examples:

• Converting an ordinary fraction to a mixed one

An improper common fraction can be converted into a mixed fraction by simple division, which results in an integer part and a remainder (fractional part).

For example, let's translate the fraction 439/31 into a mixed one:
​​

• Translation of an ordinary fraction

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 the power of 10.

For example:

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

Here, it would seem, the translation of a decimal fraction into a common one is an elementary topic, but many students do not understand it! Therefore, today we will take a closer look at several algorithms at once, with the help of which you will deal with any fractions in just a second.

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

Now let's figure it out: how to switch from decimal to normal? And most importantly: how to do it as quickly as possible?

Basic Algorithm

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

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

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

Examples of the transition from decimal notation to ordinary fractions

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

Of course. And now we will consider 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 common fraction from a decimal, you need to do the following:

1. Calculate 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 "starting" zeros on the left, if any), and $n$ is the same number of digits after the decimal point that we counted in the first step. In other words, it is necessary to divide the digits of the original fraction by one with $n$ 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, only one zero), then we get the number 64. Go to the second step: $((10)^(n))=((10)^(2))=100$, so the denominator is exactly one hundred. Well, then it remains only to reduce the numerator and denominator. :)

One more example:

Here everything is a little more complicated. Firstly, there are already 3 digits 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, then we get this: 0.004 → 0004. Recall 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 an integer part. Therefore, at the output we get an improper fraction 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 it can be done even 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 the correct fraction, then we need to remove the integer part from it for the time of transformation, and then, when we get the result, add it again to the right in front of the fractional bar.

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

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

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

That's all! The answer turned out to be the same as after the selection of 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 another technique that helps many.

Transformations by ear

Let's think about what a decimal is. More precisely, how we read it. For example, the number 0.64 - we read it as "zero integer, 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 "thousandths", i.e. 1000.

Well, what's wrong with that? And the fact that it is these numbers that eventually “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 train yourself - it's very simple. The main thing is to correctly read the original fraction. For example, 2.5 is "2 integers, 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 \u003d 10 3, and 10 \u003d 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 is decomposed only into factors 2 and 5 - it is these factors that must be sought in the numerator, so that in the end everything is reduced.

This lesson is over. Let's move on to a more complex inverse operation - see "

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. And it is necessary! 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 maths 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. This is not difficult. It is necessary to 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 an 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 how 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.

At the very beginning, you still need to find out what a fraction is and what types it is. And it comes in 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 with a horizontal dash. Both the first and the second will be equally true. The top number is called the numeral and the bottom number is the denominator. There is even a saying for those people who constantly confuse these two names. It sounds like this: “Zzzzzremember! Zzzzsignator - downzzzzu! ". This will help you not get confused. A fraction is just two numbers that are divisible by each other. The dash in them denotes 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. All you have to do is divide the numerator by the denominator. And that's it. The fraction has been translated.

The second type of fractions is called decimal. This is a series of semicolons. For example, 0.5, 3.5, etc. They called them decimal, only because after the sing, the first digit means “tens”, the second is ten times more than “hundreds”, and so on. And the first digit before the decimal point are called integers. For example, the number 2.4 sounds like this, twelve whole and two hundred and thirty-four thousandths. Such fractions appear mainly due to the fact that dividing two numbers without a remainder does not work. And most common fractions, when converted to numbers, end up as a decimal. For example, one second equals zero to five tenths.

And the final third look. These are mixed numbers. An example of this would be 2½. It sounds like two integers and one second. In high school, this type of fraction is no longer used. They will certainly need to be brought either into the ordinary form of a fraction, or into a decimal. It's just as easy to do so. Just an integer must be multiplied by the denominator and, the resulting designation, added to the numeral. Let's take our example 2½. Two multiplied by two makes four. Four plus one equals five. And a fraction of the form 2½ is formed in 5/2. And five, dividing by two, you can get a decimal fraction. 2½=5/2=2.5. It has already become clear how to translate fractions into numbers. All you have to do is divide the numerator by the denominator. If the numbers are large, you can use a calculator.

If it turns out not whole numbers and there are a lot of digits after the decimal point, then this value can be rounded. Rounding is very easy. First you need to decide which figure you want to round to. An example should be considered. A person needs to round the number zero whole, nine thousand seven hundred and fifty six ten thousandths, or in the digital value 0.6. Rounding must be done to hundredths. This means that at the moment up to seven hundredths. After the number seven in the fraction comes five. Now we need to use the rounding rules. Numbers greater than five are rounded up, and smaller numbers are rounded down. In the example, a person has five, she stands on the borderline, but it is believed that rounding is going up. So, we remove all the numbers after the seven and add one to it. It turns out 0.8.

There are also situations when a person needs to quickly convert an ordinary fraction into a number, but there is no calculator nearby. To do this, it is worth using division by a column. The first step is to write the numerator and denominator next to each other on a piece of paper. A division corner is placed between them, it looks like the letter “T”, only lying on its side. For example, take 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 is ​​four. How many sixes will be in the four, several. So, in the answer, a comma is placed after the unit, and the four is multiplied by ten. Forty-six sixes. In the answer, a six is ​​added, and thirty-six is ​​subtracted from forty. It turns out four again.

In this example, a loop has occurred, if you continue to do everything in the same way, you get the answer 1.6 (6) The number six continues for 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. Some are looping. But on the other hand, any decimal fraction can be converted into a simple one. 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 down, one whole, twenty-five divided by a hundred. One whole number is one hundred, which means that a simple fraction will be one hundred 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 were disassembled. All of them are simple, but you should know them. Fractions, especially decimals, have long been included in everyday life. This is clearly seen on the price tags in stores. Round prices have not been written for a long time, and 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 there were no fractions in Roman ones. And many scientists agree with this assumption. After all, with fractions you can conduct calculations more accurately. And in our age of space technology, accuracy in calculations is needed more than ever. So learning fractions in math school is vital to understanding many sciences and technical advances.