Published 5/12/2025
How to Convert a Fraction to a Decimal (And Back Again)
Converting a fraction to a decimal is just one division problem. Here's exactly how to do it, why some decimals repeat, and how to reverse the process.
This one is simpler than it looks. Once you see the pattern, you’ll be able to do most of them in your head.
The Core Method: Just Divide
A fraction is literally a division problem written in a different way. The fraction line means “divided by.”
So 3/4 means 3 ÷ 4. Punch that into a calculator (or by hand) and you get 0.75. Done.
More examples:
1/2= 1 ÷ 2 = 0.53/8= 3 ÷ 8 = 0.3757/10= 7 ÷ 10 = 0.75/4= 5 ÷ 4 = 1.25
The fraction and the decimal are two different ways of writing the same number. 0.75 and 3/4 are identical, just written differently.
When the Decimal Keeps Going: Repeating Decimals
Try 1/3. 1 ÷ 3 = 0.333333… and it never stops. That’s a repeating decimal.
The repeating part is usually written with a bar over it: 0.3̄ or shown as 0.333....
Common ones worth memorising:
1/3= 0.333…2/3= 0.666…1/6= 0.1666…1/7= 0.142857142857…1/9= 0.111…
Why does this happen? A fraction produces a repeating decimal when its denominator (after simplifying) has any prime factor other than 2 or 5. Since 3 is a prime factor of 3, and it’s not 2 or 5, 1/3 repeats. Since 4 = 2×2 and the only prime factor is 2, 1/4 terminates cleanly at 0.25.
A Reference Table for the Common Ones
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | Terminating |
| 1/3 | 0.333… | Repeating |
| 1/4 | 0.25 | Terminating |
| 3/4 | 0.75 | Terminating |
| 1/5 | 0.2 | Terminating |
| 2/5 | 0.4 | Terminating |
| 1/6 | 0.1666… | Repeating |
| 1/8 | 0.125 | Terminating |
| 3/8 | 0.375 | Terminating |
| 5/8 | 0.625 | Terminating |
| 7/8 | 0.875 | Terminating |
| 1/9 | 0.111… | Repeating |
How to Go the Other Way: Decimal to Fraction
For a terminating decimal:
- Write the decimal over 1:
0.75/1 - Multiply top and bottom by 10 for each decimal place (two places = ×100):
75/100 - Simplify:
75/100 = 3/4
For a repeating decimal (like 0.333...):
- Let x = 0.333…
- Multiply both sides by 10: 10x = 3.333…
- Subtract the original: 10x − x = 3.333… − 0.333… → 9x = 3
- Solve: x = 3/9 = 1/3
For a longer repeating block like 0.142857142857... (which is 1/7), you multiply by 1,000,000 instead of 10, because the repeating block is 6 digits long.
The Fast Mental Shortcut
For denominators you’ll see constantly, just memorise the decimal:
- Halves: ×0.5
- Quarters: 0.25, 0.50, 0.75
- Eighths: each eighth is 0.125, so 3/8 = 3 × 0.125 = 0.375
- Fifths: each fifth is 0.2, so 4/5 = 4 × 0.2 = 0.8
If you get stuck on any conversion, our Fraction to Decimal Converter handles it instantly with a step-by-step breakdown, including whether your result terminates or repeats and why.