Fraction to Decimal Converter

A fraction is just a division

The line in a fraction means divide. Three quarters is literally 3 divided by 4, which is 0.75, which is 75 %. All three notations describe the same quantity.

a/b = a ÷ b    and    a/b × 100 = percentage

Why some fractions never finish

A third is 0.333… and never resolves. A quarter is exactly 0.25. The rule behind this is tidy: a fraction terminates in decimal if and only if its denominator, once simplified, has no prime factors other than 2 and 5.

Those are the factors of ten, which is what decimal notation is built on. So halves, quarters, fifths, eighths, tenths, sixteenths and twentieths all terminate. Thirds, sevenths, ninths and elevenths do not, and never will in base ten.

A seventh is the famous one: 0.142857142857…, repeating those six digits forever. Multiply it by 2, 3, 4, 5 or 6 and you get the same six digits in the same cyclic order, starting at a different point.

Worth memorising

• 1/2 = 0.5 = 50 %
• 1/3 = 0.333… = 33.3 %
• 1/4 = 0.25 = 25 %
• 1/8 = 0.125 = 12.5 %
• 1/16 = 0.0625 = 6.25 %
• 1/3 of a third = 1/9 = 0.111…

The eighths matter for anyone working in inches, where 3/8 and 5/16 are everyday measurements.

Common uses

• Imperial measurements, where fractions of an inch have to become decimals for a calculator or a CAD file.
• Recipes, turning 2/3 of a cup into something a scale can show.
• Odds and probabilities, where a fraction is often more natural but a percentage is easier to compare.
• Test marks, where 17/20 is more usefully read as 85 %.

The working, step by step

Questions people ask

How do I convert a fraction to a decimal?

Divide the top number by the bottom. 3/8 is 3 ÷ 8 = 0.375.

Why do some fractions repeat forever?

A fraction terminates only if its simplified denominator has no prime factors besides 2 and 5. Thirds and sevenths do, so they recur.

What is 1/7 as a decimal?

0.142857 repeating. Those six digits cycle forever, and multiples of a seventh use the same six digits in the same order.

How do I turn it into a percentage?

Multiply the decimal by 100.

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