How do you convert a percentage to a fraction?

To convert a percentage to a fraction, write the percentage value over 100 to create the initial fraction, then simplify by dividing both numerator and denominator by their greatest common divisor. For example, 75% becomes 75/100, and since the GCD of 75 and 100 is 25, dividing both gives 3/4. For decimal percentages such as 62.5%, multiply numerator and denominator by a power of 10 to clear the decimal before simplifying.

What is 62.5% as a fraction?

62.5% expressed as a fraction is 5/8. The conversion works by writing 62.5/100, then multiplying numerator and denominator by 10 to remove the decimal: 625/1000. The GCD of 625 and 1000 is 125, so dividing both by 125 gives 5/8. As a decimal, 5 divided by 8 equals 0.625, which confirms the result.

Can all percentages be written as exact fractions?

All terminating decimal percentages (those with a finite number of decimal places, such as 62.5% or 33.33%) can be converted to exact fractions. Repeating decimals such as 33.333...% (which equals 1/3) can also be expressed as exact fractions, though they cannot be expressed as terminating decimals. This calculator handles percentages with up to several decimal places by scaling to an integer before simplifying.

Percent to Fraction Converter

This converter turns any percentage into its simplest fraction form and also shows the exact decimal equivalent and the greatest common divisor (GCD) used to reduce the fraction. Percentages and fractions are two ways of expressing the same idea: a portion of a whole. Being able to move between the two forms is useful in mathematics, cooking, finance, statistics and everyday problem solving. The conversion process starts by writing the percentage value over 100, creating an initial fraction. For whole number percentages this is straightforward; for decimal percentages such as 62.5%, the numerator contains a decimal so both the numerator and denominator must first be multiplied by the appropriate power of 10 to produce whole numbers (625 and 1000 in this case) before simplification. The resulting integer fraction is then reduced to lowest terms using the Euclidean algorithm to find the GCD, and both numerator and denominator are divided by it. The simplified fraction is shown as the main result, with the GCD and decimal as supporting figures. To use the converter, type any percentage into the input field, including decimals such as 12.5 or 66.67. The result updates immediately. You do not need to type the percent symbol. This tool is useful for students converting between fraction and percentage forms, teachers preparing worked examples, and anyone checking whether a percentage such as a discount or interest rate can be expressed as a simple fraction. Results are as precise as the number of decimal places in your input allows.

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Percentage

5/8

simplest fraction

Decimal0.625

GCD used125

Before simplifying625/1000

How it works

The calculator reads the percentage value and counts the number of decimal places in it. It multiplies the percentage by 10 raised to that count to produce a whole number, and multiplies 100 by the same factor for the denominator. This produces an equivalent integer fraction. The Euclidean algorithm then finds the GCD of the numerator and denominator, and both are divided by the GCD to give the lowest terms fraction. A GCD of 1 means the fraction was already in its simplest form after scaling.

Worked example

Convert 62.5% to a fraction. The decimal has one decimal place, so multiply both parts by 10: numerator = 625, denominator = 1000. The initial fraction is 625/1000. Find the GCD: GCD(625, 1000) = 125. Divide both by 125: numerator = 625 ÷ 125 = 5, denominator = 1000 ÷ 125 = 8. The simplified fraction is 5/8. As a decimal: 5 ÷ 8 = 0.625, which confirms the result matches the original percentage.

Related calculators

Simplify Fractions: reduce any numerator and denominator to lowest terms.
Mixed Numbers Calculator: add, subtract, multiply or divide mixed numbers.
Percentage Calculator: work out percentage change, part of a whole, and what percent one number is of another.
Percent Error Calculator: find the percentage difference between a measured and true value.

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