To convert a fraction to a decimal, divide the numerator by the denominator. The numerator is the top number; the denominator is the bottom number. For example, 7/8 means 7 ÷ 8, which equals 0.875. Keep the order the same when using a calculator.
Some divisions finish, while others produce a repeating pattern. Both can represent an exact answer, but a shortened decimal may only be an approximation. The examples below show how to do the division, predict whether it ends, and choose the right way to write the result.
How to divide a fraction by hand
Work through 7/8. Since 7 is smaller than 8, the whole-number part is 0. Write 7 as 7.000 and place a decimal point after the 0 in your answer. Adding zeros after a decimal point does not change the original value.
First decimal place: think of the 7 wholes as 70 tenths. Eight goes into 70 eight times, using 64 tenths and leaving 6 tenths. Write 8 in the tenths place, so the answer starts 0.8.
Second decimal place: the remaining 6 tenths are 60 hundredths. Eight goes into 60 seven times, using 56 and leaving 4. Write 7 in the hundredths place: 0.87.
Third decimal place: the remaining 4 hundredths are 40 thousandths. Eight goes into 40 five times with nothing left over. Write 5 in the thousandths place. The final answer is 7/8 = 0.875. Check by multiplying: 0.875 × 8 = 7.
This is the division method described in OpenStax’s lesson on decimals and fractions. The useful stopping signal is a zero remainder, not a particular number of decimal places.
A shortcut: make the denominator 10, 100 or 1,000
Sometimes equivalent fractions are quicker than long division. For 13/20, multiply both numbers by 5: 13/20 = 65/100 = 0.65. Multiplying only the denominator would change the fraction, so always change both parts by the same factor.
For 9/40, multiply both numbers by 25. You get 225/1,000, or 0.225. The three zeros in 1,000 tell you to use three decimal places. This also explains why 3/100 is 0.03 rather than 0.3: it means three hundredths, not three tenths.
What if the division keeps going?
Try 5/6. Dividing 50 tenths by 6 gives 8 tenths with remainder 2 tenths. Convert that remainder to 20 hundredths: 6 goes into 20 three times and leaves 2 hundredths. The same step happens again at the next place.
The answer is 0.8333…, with the 3 repeating forever. The 8 does not repeat. You can also write “0.8 followed by repeating 3s” when a keyboard makes an overbar awkward. A repeating decimal has a digit or group of digits that continues endlessly.
A repeated remainder explains the pattern: the next division starts from the same remainder, so it produces the same next digit and remainder again. There are only finitely many possible remainders for a fixed positive integer denominator. Division therefore either reaches zero or eventually repeats.
How to tell whether a decimal will terminate
Reduce the fraction first. Its decimal terminates if the positive denominator in lowest terms has no prime factors other than 2 and 5. A denominator of 1 gives a whole number. If another prime factor remains, the decimal repeats. NRICH’s “Terminating or Not” investigation explores this rule.
For example, 11/40 terminates because 40 = 2 × 2 × 2 × 5. But 11/30 repeats because 30 includes a factor of 3. Meanwhile, 9/24 simplifies to 3/8, so it terminates despite the factor of 3 in the original denominator.
The reason is the decimal system itself: a terminating decimal can be written over 10, 100, 1,000 or another power of 10. Those denominators contain only factors of 2 and 5. Reducing the fraction removes factors that were never needed to represent its value.
Mixed numbers, improper fractions and negative signs
For a positive mixed number, keep the whole-number part and convert the fractional part. Since 7/8 = 0.875, 2 7/8 = 2.875. Alternatively, convert the mixed number to 23/8 and divide 23 by 8. Both routes agree.
An improper fraction can produce a decimal greater than 1. For example, 19/8 = 2.375. Do not automatically put 0 before the decimal just because the original number was written as a fraction.
For a negative fraction, divide the magnitudes and apply the sign: −7/8 = −0.875. A negative mixed number such as −2 7/8 means −(2 + 7/8), so it is −2.875, not −1.125. One negative sign gives a negative result; two negatives give a positive result.
Exact answers versus rounded answers
A terminating answer such as 0.875 is exact. So is 0.8333… when the notation explicitly means the 3s continue forever. However, 0.83 is only a rounded version of 5/6. Write 5/6 ≈ 0.83 to show approximation.
To round to two decimal places, inspect the third digit. In 0.875, that digit is 5, so ordinary school rounding gives 0.88. For 0.8333…, the third digit is 3, so the answer stays 0.83. Keep extra digits during a longer calculation and round at the end.
Check your answer before moving on
For a positive proper fraction, expect a result between 0 and 1. If your answer is greater than 1, check whether you divided in reverse. A zero numerator gives 0 when the denominator is nonzero; a zero denominator is undefined and cannot be converted.
Try these independently: 17/20, 7/16 and 2 3/5. The answers are 0.85, 0.4375 and 2.6. Multiplying each decimal by its denominator checks the first two. For the mixed number, subtract 2 and check that 0.6 × 5 = 3.
For paper practice, an ordinary pencil and notebook are enough. You can browse graph-paper notebooks on Amazon if you want columns that help keep decimal places aligned.
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