How to Convert a Decimal to a Fraction

A decimal is already a fraction written another way. The digits after the decimal point are the top, and a power of 10 (10, 100, 1,000, …) is the bottom. Then you simplify.

Try it with your own problem ↓

The steps

Count the digits after the decimal point.
Write those digits (without the point) as the numerator.
Write 1 followed by that many zeros as the denominator: one digit gives tenths, two give hundredths, three give thousandths.
Simplify by dividing the top and bottom by their GCF.
If there is a whole number part, keep it in front as a mixed number.

A worked example

Write 0.375 as a fraction.

There are 3 digits after the decimal point, so the denominator is 1,000.
The digits are 375, so the fraction is 375/1000.
The GCF of 375 and 1000 is 125 (375 = 3 × 125 and 1000 = 8 × 125).
Divide both by 125: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8.

0.375 = 375/1000 = 3/8.

Why it works

Place value names the denominator for you. In 0.375 the 3 is in the tenths place, the 7 in the hundredths and the 5 in the thousandths, so the whole thing is 375 thousandths. Saying it aloud, "three hundred seventy-five thousandths", gives you 375/1000 straight away.

Try it with your own problem

Open the free The Fraction Bar with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 0.375 as a fractionOpens The Fraction Bar with this example

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Common mistakes

Using the wrong power of 10. 0.375 has three decimal places, so the denominator is 1,000, not 100.
Dropping a zero. 0.05 is 5/100 = 1/20, not 5/10.
Not simplifying. 375/1000 is right, but most teachers want 3/8.
Forgetting the whole number. 2.45 is 2 9/20, not 9/20.

Questions people ask

How do I write a decimal with a whole number part, like 2.45?

Write the whole number, then the decimal part as a fraction: 2 and 45/100, which simplifies to 2 9/20. As an improper fraction, that is 49/20.

What if the decimal repeats?

Repeating decimals need an algebra trick: 0.333… is 1/3. Use the fractions helper below to see the steps.

What is 0.5 as a fraction?

5/10, which simplifies to 1/2.

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