Fractions to Decimals and Percents: A Simple Guide

A fraction, a decimal and a percent are three ways of writing the same amount. Half a pizza is 1/2, 0.5 or 50% of it. Moving between them takes only two ideas: a fraction means division, and a percent means "out of 100".

Step 1: Divide

Divide the top number by the bottom number. 5/8 means 5 ÷ 8. By long division, write 5 as 5.000 and work one digit at a time:

50 ÷ 8 = 6, remainder 2
20 ÷ 8 = 2, remainder 4
40 ÷ 8 = 5, remainder 0

The digits give 0.625, and the division ends because the remainder hit 0.

Step 2: Multiply by 100

To get a percent, multiply the decimal by 100, which moves the decimal point two places right. 0.625 becomes 62.5%.

Will it end or go on forever?

Simplify the fraction, then factor the bottom number:

• Only 2s and 5s? The decimal ends. 9/40 = 0.225, because 40 = 2³ × 5.
• Any other prime? The decimal repeats forever. 7/12 = 0.58333…, because 12 contains a 3.

When repeating, the cycle starts as soon as a remainder in the long division comes back a second time. 4/11 gives remainders 4, 7, 4, 7 … so the decimal is 0.3636…

The denominator-of-100 trick

If you can turn the bottom into 100, the top is the percent. 13/20: multiply top and bottom by 5 to get 65/100, so 65%. 9/25: multiply by 4 to get 36/100, so 36%.

Reference table

Tip Keep all the digits until the very last step. Rounding 7/12 to 0.58 before multiplying gives 58%, but the true value is closer to 58.33%.

½Try it yourself: Fraction to Decimal & Percent CalculatorChange a fraction into a decimal and a percent with long division, marking any digits that repeatOpen →

Common questions