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Converting a fraction to a decimal. How to Convert Fractions and Percents to Decimals

They are used extremely widely, and in the most various fields human activity be it scientific and applied computing, development and operation various equipment, economic calculation and so on. In mind various kinds reasons it is often necessary to carry out decimal conversion, as well as the reverse process. It should be noted that similar transformation are produced relatively easily, and in accordance with certain rules and techniques that have existed in mathematics for many hundreds of years.

Converting a decimal fraction to a prime fraction

Decimal conversion into the “ordinary” fraction it is quite easy and simple. To do this, the following technique is used: the number located to the right of the decimal point is taken as the numerator of the new fraction original number, the number ten is used as the denominator, to a power equal to the number of digits in the numerator. As for the remaining whole part, it remains unchanged. If the integer part is equal to zero, then after the transformation it is simply omitted.

EXAMPLE 1

Fifty point twenty five equals fifty point one and twenty five divided by one hundred equals fifty point one fourth.

Converting a fraction to a decimal

Converting a Fraction to a Decimal, in fact, is the inverse converting a decimal fraction into a prime fraction. Its implementation also does not cause any difficulties and is, in fact, quite simple. arithmetic operation. In order to convert a fraction to a decimal you need to divide the numerator by its denominator in accordance with certain rules.

EXAMPLE 1

Need to implement fraction conversion five eighths in decimal.

Dividing five by eight gives decimal zero point six hundred twenty-five thousandths.

= 0.625

Rounding the result of converting a fraction to a decimal

It should be noted that, unlike a process such as decimal conversion, this procedure can often last indefinitely. In such cases they say that the result of the procedure converting a fraction to a decimal may not be accurate. However, practice shows that in the vast majority of cases the receipt is ideal exact result and is not required. As a rule, the division process ends when it has already obtained the values ​​of those decimal fractions that are of practical interest in each specific case.

EXAMPLE 1

You need to cut a piece of butter weighing one kilogram into nine pieces of equal weight. When performing this procedure, it turns out that the mass of each of them is 1/9 kilogram. If carried out according to all the rules transformation this common fraction V decimal fraction, then it turns out that the mass of each of the resulting parts is equal to zero whole and one in the period of a kilogram.

Rounding is carried out according to standard rules provided in arithmetic: if the first of the “discarded” digits has a value of 5 or more, then the last of the significant ones is increased by one. Otherwise it remains unchanged.

EXAMPLE 2

Convert fraction one eighth to a decimal fraction.

When one is divided by eight, the result is zero point one hundred twenty-five thousandths, or rounded - zero point thirteen hundredths.

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 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 = 5. Therefore, any whole number can be written as an ordinary improper fraction or a series of such fractions. Let's consider records of the same number as a series 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. Decimal notation looks like this:

Rules for converting between different types of fractions

  • Converting a mixed fraction to a common fraction

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:


An improper fraction can be converted to mixed by simple division, which results in the integer 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 decimal. For example, the fraction 1/3 when divided will never give the final result.

A decimal fraction consists of two parts, separated by commas. The first part is a whole unit, the second part is tens (if there is one number after the decimal point), hundreds (two numbers after the decimal point, like two zeros in a hundred), thousandths, etc. Let's look at examples of decimal fractions: 0, 2; 7, 54; 235.448; 5.1; 6.32; 0.5. These are all decimal fractions. How to convert a decimal fraction to an ordinary fraction?

Example one

We have a fraction, for example, 0.5. As mentioned above, it consists of two parts. The first number, 0, shows how many whole units the fraction has. In our case there are none. The second number shows tens. The fraction even reads zero point five. Decimal number convert to fraction Now it won’t be difficult, we write 5/10. If you see that the numbers have common divisor, you can reduce the fraction. We have this number 5, dividing both sides of the fraction by 5, we get - 1/2.

Example two

Let's take more complex fraction- 2.25. It reads like this: two point two and twenty-five hundredths. Please note - hundredths, since there are two numbers after the decimal point. Now you can convert it to a common fraction. We write down - 2 25/100. The whole part is 2, the fractional part is 25/100. As in the first example, this part can be shortened. The common factor for the numbers 25 and 100 is the number 25. Note that we always choose the greatest common factor. Dividing both sides of the fraction by GCD, we got 1/4. So 2.25 is 2 1/4.

Example three

And to consolidate the material, let’s take the decimal fraction 4.112 - four point one and one hundred and twelve thousandths. Why thousandths, I think, is clear. Now we write down 4 112/1000. Using the algorithm, we find the gcd of the numbers 112 and 1000. In our case, this is the number 6. We get 4 14/125.

Conclusion

  1. We break the fraction into whole and fractional parts.
  2. Let's see how many digits are after the decimal point. If one is tens, two is hundreds, three is thousandths, etc.
  3. We write the fraction in ordinary form.
  4. Reduce the numerator and denominator of the fraction.
  5. We write down the resulting fraction.
  6. We check and divide top part fractions to the bottom. If there is an integer part, add it to the resulting decimal fraction. The original version turned out great, which means you did everything right.

Using examples, I showed how you can convert a decimal fraction to an ordinary fraction. As you can see, this is very easy and simple to do.

Often children who study at school are interested in why they go to school. real life Mathematics may be required, especially those sections that already go much further than simple counting, multiplication, division, addition and subtraction. Many adults also ask this question if they professional activity very far from mathematics and various calculations. However, it is worth understanding that there are all sorts of situations, and sometimes it is impossible to do without that very notorious school curriculum that we so disdainfully rejected in childhood. For example, not everyone knows how to convert a fraction into a decimal, but such knowledge can be extremely useful for ease of calculation. First, you need to make sure that the fraction you need can be converted to a final decimal. The same goes for percentages, which can also be easily converted to decimals.

Checking a fraction to see if it can be converted to a decimal

Before you count anything, you need to make sure that the resulting decimal fraction will be finite, otherwise it will turn out to be infinite and it will simply be impossible to calculate the final version. Moreover infinite fractions can also be periodic and simple, but this is a topic for a separate section.

It is possible to convert an ordinary fraction into its final, decimal version only if its unique denominator can only be expanded into factors of 5 and 2 ( prime factors). And even if they are repeated an arbitrary number of times.

Let us clarify that both of these numbers are prime, so in the end they can be divided without a remainder only by themselves, or by one. Table prime numbers can be found without problems on the Internet, it is not at all difficult, although it has no direct relation to our account.

Let's look at examples:

The fraction 7/40 can be converted from a fraction to its decimal equivalent because its denominator can be easily factored into factors of 2 and 5.

However, if the first option results in a final decimal fraction, then, for example, 7/60 will in no way give a similar result, since its denominator will no longer be decomposed into the numbers we are looking for, but will have a three among the denominator factors.

There are several ways to convert a fraction to a decimal

Once it has become clear which fractions can be converted from ordinary to decimal, you can begin with the conversion itself. In fact, there is nothing super difficult, even for someone whose school curriculum has completely faded from memory.

How to convert fractions to decimals: the easiest method

This method of converting a fraction into a decimal is indeed the simplest, but many people are not even aware of its mortal existence, since at school all these “truths” seem unnecessary and not very important. Meanwhile, not only an adult will be able to figure it out, but a child will also easily perceive such information.

So, to convert a fraction to a decimal, you multiply the numerator, as well as the denominator, by one number. However, everything is not so simple, as a result, it is in the denominator that you should get 10, 100, 1000, 10,000, 100,000 and so on, ad infinitum. Don’t forget to first check whether a given fraction can be converted to a decimal.

Let's look at examples:

Let's say we need to convert the fraction 6/20 to a decimal. We check:

After we are convinced that it is still possible to convert a fraction into a decimal fraction, and even a finite one, since its denominator can easily be decomposed into twos and fives, we should proceed to the translation itself. The most the best option, logically, to multiply the denominator and get the result 100 is 5, since 20x5=100.

You can consider an additional example for clarity:

The second and more popular method convert fractions to decimals

The second option is somewhat more complicated, but it is more popular due to the fact that it is much easier to understand. Everything here is transparent and clear, so let’s move on to the calculations right away.

Worth remembering

In order to correctly convert a simple, that is, ordinary fraction into its decimal equivalent, you need to divide the numerator by the denominator. In fact, a fraction is a division, you can’t argue with that.

Let's look at the action using an example:

So, the first thing to do is to convert the fraction 78/200 to a decimal, you need to divide its numerator, that is, the number 78, by the denominator 200. But the first thing that should become a habit is to check, which was already mentioned above.

After checking, you need to remember the school and divide the numerator by the denominator with a “corner” or “column”.

As you can see, everything is extremely simple, and you don’t need to be a genius to easily solve such problems. For simplicity and convenience, we also provide a table of the most popular fractions that are easy to remember and don’t even make an effort to translate them.

How to convert percentages to decimals: nothing is simpler

Finally, the move has come to percentages, which, it turns out, as the same school curriculum says, can be converted into a decimal fraction. Moreover, everything will be much simpler here, and there is no need to be afraid. Even those who did not graduate from universities, skipped the fifth grade of school and know nothing about mathematics, can cope with the task.

Perhaps we need to start with a definition, that is, understand what interest actually is. A percentage is one hundredth of a number, that is, completely arbitrary. From a hundred, for example, it will be one and so on.

Thus, to convert percentages to a decimal, you simply need to remove the % sign, and then divide the number itself by a hundred.

Let's look at examples:

Moreover, in order to make a reverse “conversion”, you simply need to do everything the other way around, that is, you need to multiply the number by a hundred and attach a percent sign to it. In exactly the same way, by applying the acquired knowledge, you can also convert an ordinary fraction into a percentage. To do this, it will be enough to simply first convert an ordinary fraction into a decimal, and therefore convert it into a percentage, and you can also easily perform the reverse action. As you can see, there is nothing super complicated, all this is basic knowledge that just needs to be kept in mind, especially if you are dealing with numbers.

The path of least resistance: convenient online services

It also happens that you don’t want to count at all, and you simply don’t have the time. It is for such cases, or especially lazy users, that there are many convenient and easy-to-use services on the Internet that will allow you to convert ordinary fractions, as well as percentages, into decimal fractions. This is truly the path of least resistance, so using such resources is a pleasure.

Useful reference portal "Calculator"

In order to use the Calculator service, simply follow the link http://www.calc.ru/desyatichnyye-drobi.html and enter the required numbers in the required fields. Moreover, the resource allows you to convert both ordinary and mixed fractions to decimals.

After a short wait, about three seconds, the service will display the final result.

In exactly the same way, you can convert a decimal fraction to a regular fraction.

Online calculator on the “Mathematical resource” Calcs.su

Another very useful service can be called a fraction calculator on the “Mathematical resource. Here you also don’t have to count anything yourself, just select from the list provided what you need and go ahead and get the orders.

Next, in the field provided specifically for this, you need to enter the desired number of percentages, which need to be converted into a regular fraction. Moreover, if you need decimal fractions, then you can easily cope with the translation task yourself or use the calculator that is designed for this.

Ultimately, it’s worth adding that no matter how many newfangled services are invented, no matter how many resources offer you their services, it won’t hurt to train your head periodically. Therefore, you should definitely apply the knowledge you have acquired, especially since you can then proudly help your own children and then grandchildren do their homework. For those who suffer from an eternal lack of time, such online calculators on mathematical portals will come in handy and will even help you understand how to convert a fraction to a decimal.

Very often in school curriculum Mathematicians children are faced with the problem of how to convert a fraction to a decimal. In order to convert a common fraction to a decimal, let us first remember what a common fraction and a decimal are. An ordinary fraction is a fraction of the form m/n, where m is the numerator and n is the denominator. Example: 8/13; 6/7, etc. Fractions are divided into regular, improper and mixed numbers. A proper fraction is when the numerator is less than the denominator: m/n, where m 3. An improper fraction can always be represented as a mixed number, namely: 4/3 = 1 and 1/3;

Converting a fraction to a decimal

Now let's look at how to translate mixed fraction to decimal. Any ordinary fraction, whether proper or improper, can be converted to a decimal. To do this, you need to divide the numerator by the denominator. Example: simple fraction(correct) 1/2. Divide numerator 1 by denominator 2 to get 0.5. Let's take the example of 45/12; it is immediately clear that this is an irregular fraction. Here the denominator is less than the numerator. We transform improper fraction to decimal: 45: 12 = 3.75.

Converting mixed numbers to decimals

Example: 25/8. First we transform mixed number into an improper fraction: 25/8 = 3x8+1/8 = 3 and 1/8; then divide the numerator equal to 1 by the denominator equal to 8, using a column or on a calculator and get a decimal fraction equal to 0.125. The article provides the easiest examples of conversion to decimal fractions. Having understood the translation technique into simple examples, you can easily solve the most difficult of them.