In short: To convert a fraction to a decimal, divide the top number by the bottom number. So 3/8 means 3 divided by 8, which gives 0.375. If the bottom number turns easily into 10, 100 or 1000, you can instead scale the fraction up and read the decimal straight off.
Knowing how to convert a fraction to a decimal is a core GCSE Foundation skill that helps with ordering numbers, percentages and probability. There are two reliable ways to do it: short division, which always works, and equivalent fractions, which is a quick shortcut for friendly denominators. This guide shows both by hand, with a worked example you can follow.
The reliable method
The fraction bar means "divide", so any fraction can become a decimal.
- Read the fraction as top divided by bottom. The fraction 3/8 means 3 ÷ 8.
- Set up a short division with the top number inside and the bottom number outside.
- Add a decimal point and zeros to the top number, so 3 becomes 3.000.
- Divide as normal, carrying remainders across. Keep going until there is no remainder, or until the digits start repeating.
- Line up the decimal point in your answer with the one in the number you are dividing.
For a quick shortcut, check whether the bottom number divides into 10, 100 or 1000. If it does, scale the whole fraction up to that denominator and the top number becomes the decimal. For example, 2/5 scales to 4/10 = 0.4.
A worked example
Convert the fraction 3/8 into a decimal.
The bottom number 8 does not divide neatly into 10 or 100, so we use short division: 3 ÷ 8.
Write 3 as 3.000 and divide by 8:
- 8 into 3 does not go, so write 0 and carry the 3. Place the decimal point: 0.
- 8 into 30 goes 3 times (3 × 8 = 24), remainder 6. So far: 0.3
- 8 into 60 goes 7 times (7 × 8 = 56), remainder 4. So far: 0.37
- 8 into 40 goes 5 times (5 × 8 = 40), remainder 0. So far: 0.375
There is no remainder, so the division stops. 3/8 = 0.375.
This works because dividing the top by the bottom shares 3 whole units into 8 equal parts, and each part is 0.375 of a unit. Adding zeros after the decimal point just lets you keep dividing into smaller and smaller place values.
Common mistakes to avoid
- Trap: dividing the wrong way round. Working out 8 ÷ 3 instead of 3 ÷ 8. Fix: always divide the top number by the bottom number.
- Trap: losing the decimal point. Writing 375 instead of 0.375. Fix: place the decimal point in the answer directly above the one in the number you are dividing.
- Trap: stopping too early on a recurring decimal. Some fractions, like 1/3, never end. Fix: once a digit repeats, write it with a dot above, such as 0.3 recurring.
- Trap: muddling the place values of the decimal answer. Reading 0.375 as "nought point three hundred and seventy-five". Fix: see [decimal place value explained](/misconceptions/decimal-place-value) to keep tenths, hundredths and thousandths straight.
Frequently asked questions
How do you turn a fraction into a decimal by hand? Divide the top number by the bottom number using short division. Add a decimal point and zeros to the top number, then divide as usual, carrying any remainders. For example, 3 ÷ 8 gives 0.375.
What is 3/4 as a decimal? 3/4 means 3 ÷ 4, which equals 0.75. You can also scale it up: 3/4 is the same as 75/100, and 75 hundredths is 0.75.
How do you convert a fraction with a denominator like 5 or 10? Scale it to a denominator of 10, 100 or 1000. For 2/5, multiply top and bottom by 2 to get 4/10, which is 0.4. This is faster than dividing when the bottom number fits neatly.
Why do some fractions give recurring decimals? A fraction recurs when its division never reaches a remainder of zero. For example, 1/3 divides as 0.3333... forever, written as 0.3 with a dot above the 3 to show it repeats.
Is dividing always reliable for converting fractions? Yes. Short division works for every fraction, including awkward ones. The equivalent-fractions shortcut is faster but only works when the denominator divides easily into 10, 100 or 1000.
Practise this
Find out which mistakes cost marks — [take the free diagnostic](/diagnostic). Related: [decimal place value explained](/misconceptions/decimal-place-value).