Fraction To Decimal Calculator

What this calculator does

So, you have a fraction like 3/4 and you want it as a decimal, 0.75. This tool does that in one step by dividing the top by the bottom, and it shows the result rounded to two decimal places.

There are two boxes, a numerator and a denominator. Type the fraction and read off its decimal value.

How to use it

1. Type the numerator, the top number.
2. Type the denominator, the bottom number.
3. Press Calculate.

The denominator cannot be zero, since dividing by zero has no value. Everything else it will take and divide.

The fraction bar is a division sign

The key to this conversion is realising the fraction bar was a division sign all along. 3/4 does not just look like three over four, it means three divided by four. That is why every fraction has a decimal value: you simply carry out the division the fraction has been describing. Three quarters means splitting 3 into 4 equal parts, and each part is 0.75.

The method it uses

Divide the numerator by the denominator. That single division is the whole conversion. 3 divided by 4 is 0.75, so 3/4 is 0.75. 1 divided by 8 is 0.125, so 1/8 is 0.125. The tool rounds the answer to two decimal places for a clean read, so a value like 1/3, whose decimal never ends, is shown as 0.33.

A worked example, step by step

Take 5/8.

• Divide the top by the bottom: 5 ÷ 8.
• That equals 0.625.
• So 5/8 is 0.625, shown rounded to 0.63 at two places.

The same one-step division turns 7/10 into 0.7 and 9/4 into 2.25.

Why some come out clean and some run on

Divide 3 by 4 and you get exactly 0.75, but divide 1 by 3 and you get 0.3333... going on forever. Both are correct; the difference is in the denominator. A fraction gives a clean, terminating decimal only when its denominator, in lowest terms, is built from just 2s and 5s, the factors of 10. 4 is two 2s, and 8 is three 2s, so quarters and eighths land neatly. A 3 or a 7 on the bottom cannot divide evenly into any power of 10, so those decimals repeat without end. Since a display cannot show an endless decimal, the tool rounds to two places, which is why 1/3 appears as 0.33 rather than trailing on.

The reverse trip: decimal to fraction

This tool goes from a fraction to a decimal. To go the other way, from a decimal back to a fraction, you write the decimal over a power of 10 and reduce, which the decimal to fraction calculator does. A fraction, a decimal, and a percent are three ways of writing the same value, and each conversion just moves between two of those forms.

Questions people ask

How does it turn a fraction into a decimal?

By dividing the numerator by the denominator. The fraction bar means division, so carrying out that division gives the decimal value.

How many decimal places does it show?

Two. A value with a longer or endless decimal, such as 1/3, is rounded, so it appears as 0.33.

Why does 1/3 never come out exact?

Because 3 does not divide evenly into any power of 10. Only denominators made from 2s and 5s give terminating decimals; others repeat forever.

Why can't the denominator be zero?

Because dividing by zero has no defined value. The tool asks for a nonzero denominator before it will divide.

How do I turn a decimal back into a fraction?

Use the decimal to fraction calculator, which writes the decimal over a power of 10 and reduces it. It is the inverse of this tool.

References

On dividing a fraction out and on decimals that repeat. Every fraction is a division waiting to be carried out, and the result either terminates or falls into an endlessly repeating pattern, depending on the denominator.

1. Eric W. Weisstein, "Repeating Decimal," from MathWorld, a Wolfram resource, on why some fractions give endless, repeating decimals.
2. Eric W. Weisstein, "Fraction," from MathWorld, a Wolfram resource, on the numerator, denominator, and the fraction as a division.