A fraction is a division problem in disguise: 3/8 means 3 ÷ 8. To get the decimal, divide the top by the bottom with long division, adding zeros after the decimal point as needed.
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The steps
- Write the fraction as a division: the numerator is the dividend and the denominator is the divisor.
- Put a decimal point after the numerator and add zeros: 3 becomes 3.000.
- Do long division. Put the decimal point in the answer directly above the one in the dividend.
- Keep going until the remainder is 0 (a terminating decimal) or the digits start to repeat (a repeating decimal).
- If you only need a rounded answer, stop and round.
A worked example
Convert 3/8 to a decimal.
- Set up 3 ÷ 8 as 3.000 ÷ 8. Since 8 doesn't go into 3, the answer starts 0.
- Bring in a tenth: 30 ÷ 8 = 3, because 8 × 3 = 24, with 30 − 24 = 6 left over.
- Bring down a zero: 60 ÷ 8 = 7, because 8 × 7 = 56, with 60 − 56 = 4 left over.
- Bring down a zero: 40 ÷ 8 = 5, because 8 × 5 = 40, with 0 left over.
- The remainder is 0, so we stop. The digits are 3, 7, 5.
3/8 = 0.375. Check: 0.375 × 8 = 3. ✓
Common mistakes
- Dividing the bottom by the top. 3/8 is 3 ÷ 8, not 8 ÷ 3.
- Forgetting the decimal point. It goes in the answer right above the decimal point in the dividend.
- Rounding a repeating decimal as if it ended. 2/3 = 0.666…, not 0.66. Write 0.6 with a bar over the 6, or say "about 0.67".
- Stopping too soon. Keep adding zeros until the remainder is 0 or a pattern repeats.
Questions people ask
Which fractions give repeating decimals?
In lowest terms, a fraction repeats if its denominator has any prime factor other than 2 or 5. 1/3, 1/6 and 1/7 repeat; 1/2, 1/4 and 3/8 end.
What is 2/3 as a decimal?
0.666…, with the 6 repeating forever. Rounded to two places it is 0.67.
How do I turn a decimal back into a fraction?
Use the place value: 0.375 is 375/1000, which simplifies to 3/8.
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