How to convert a fraction to decimal

1. Convert the denominator to 10, 100, or 1,000

This method is very simple, but it doesn't work for every fraction.

First, multiply the numerator and denominator by a number that converts the bottom of the fraction to 10 or 100, 1,000, and so on.

How to convert a fraction to decimal: convert the denominator to 10, 100, or 1,000

Let's say we need to translate a fraction with numerator 7 and denominator 25. We can get 100 in the lower part: it is enough to multiply 25 by 4. Don't forget about the upper part: we get 28.

Write down the numerator separately. Count on the right in it as many digits as the zeros you got in the denominator after multiplying, and put a comma. This will be the desired decimal fraction.

How to convert a fraction to decimal: separate as many digits as there were zeros with a comma

In our example, the denominator is 100, which means we count two digits in the numerator and put a comma. We get 0, 28.

If such a multiplier cannot be found, the current method will not work. Use the following.

2. Divide the numerator by the denominator

To convert an ordinary fraction to a decimal, it is enough to divide its upper part by the lower one. The easiest way to do this, of course, is with a calculator.

If it is fundamentally important for you to do without assistive devices, simply divide the numerator by the denominator in a column.

How to convert a fraction to decimal: divide the numerator by the denominator

For example, let's translate the fraction with numerator 7 and denominator 25. Dividing 7 by 25 with a column, we get 0, 28.

An important point. When dividing by a long line, you may find that the process goes in a circle and after the decimal point, repeating numbers fall into the result. In this case, this fraction cannot be converted to a final decimal. Instead, you will end up with a periodic fraction. To record the result, put the repeating number in parentheses.

If you get a periodic fraction, put the repeating number in parentheses

Let's say you need to convert a fraction with numerator 1 and denominator 3. Dividing 1 by 3 with a column, we get an infinite decimal fraction 0, 333333333 … Bring it to a short form 0, (3) - this will be the result. It reads as "zero point and three in the period."