Fraction to Decimal Calculator

How to convert a fraction to decimal

Decimal numbers began to be used for more convenient writing of fractions. To write a decimal number, you need to separate the whole-number part and the fractional part with a comma. If the fraction does not contain a whole-number part, you must put a zero in front of the comma. If the fraction has a denominator like 10, 100, 1000, etc. and the number of digits in the numerator is less than in the denominator, then to convert such a number into a fraction it is necessary to count the number of digits in the numerator and the number of zeros in the denominator. For example, the fraction (zero point 12 thousandths) 2 digits in the numerator and 3 zeros in the denominator. 3 - 2 = 1, therefore, it is necessary to write one zero after the decimal point:

	12	= 0,012
	1000

Let's give another example, the fraction

	3
	1000

This fraction has 1 digit in the numerator, 3 zeros in the denominator. 3 - 1 = 2, therefore, it is necessary to write two zeros after the decimal point:

	3	= 0,003
	1000

And the last example, fraction

	12
	100

This fraction has 2 digits in the numerator and 2 zeros in the denominator. 2 - 2 = 0, therefore, no need to add a zero after the decimal point:

	12	= 0,12
	100

If the denominator of a fraction is a number other than numbers like 10, 100, 1000, etc., then it is necessary to make the denominator of such a fraction like 10, 100, 1000, etc. The first step is to simplify the fraction. Then expand the denominator of the fraction into prime factors. If the expansion contains at least one factor other than 2 or 5, then such a fraction can only be represented as an infinite decimal number. If in the expansion of a fraction all factors are numbers 2 or 5, then it is necessary to make sure that the number of twos and fives is the same. To do this, you need to multiply the numerator and denominator of the fraction by the missing number of twos or fives. For example,

	1	=
	40

	1	=
	2∙2∙2∙5

	1∙5∙5	=
	2∙2∙2∙5∙5∙5

	25	=
	1000

0.025

Let's give another example

5	301	=
	200

6	101	=
	200

6	101	=
	2∙2∙2∙5∙5

6	101∙5	=
	2∙2∙2∙5∙5∙5

6	505	=
	1000

6.505

Let's give an Example of an infinite decimal

	1	=
	3

0.333333333333333...

When converting this fraction to a decimal number, an infinite decimal number is obtained.