Decimal to Fraction Calculator
Every terminating decimal is already a fraction over a power of ten. The only work is cancelling it down.
As a fraction
5/8
- Fraction
- 5/8
- Mixed number
- —
- Percentage
- 62.5000%
- Check
- 0.625000
- Every terminating decimal is a fraction over a power of ten — 0.75 is 75/100 — and the only work is cancelling it down. 75 and 100 share a factor of 25, so it becomes 3/4.
- Repeating decimals are a different problem and this does not attempt them. Type 0.333 and you get 333/1000, which is exactly what you typed rather than a third.
About converting decimals to fractions
The place values do the work. 0.625 is 625 thousandths, so the fraction is 625/1000 before anything is simplified. Both parts divide by 125, which gives 5/8.
That is the whole method: count the decimal places, put the digits over one followed by that many zeros, then reduce. Three places means over a thousand, two means over a hundred. The reduction is where the tidy answer comes from.
This handles terminating decimals only, and that limitation is worth being explicit about. Type 0.333 and you get 333/1000, because that is exactly the number you typed. Recognising it as a third would mean guessing that you meant a repeating decimal, and a calculator that guesses is worse than one that does not.
Some fractions are useful to recognise on sight, because they come up constantly in measurements and prices. 0.5 is a half, 0.25 a quarter, 0.125 an eighth, 0.0625 a sixteenth. Anything ending in .5 of an inch, and every halving after it, follows that pattern.
What it works out
- A decimal as a fraction in lowest terms
- The mixed number form
- The percentage equivalent
The formula
Fraction = Digits ÷ 10^(number of decimal places), then reduced
0.625 has three decimal places, so it is 625 over 10³ — 625/1000.
Reducing needs the greatest common divisor of 625 and 1000, which is 125. Dividing both by it gives 5/8, and 5 and 8 share no factor, so that is as far as it goes.
The number of places is the only thing that changes. 0.4 is 4/10, which reduces to 2/5. 0.0625 is 625/10000, which reduces to 1/16.
Repeating decimals need a different method entirely — you multiply by a power of ten, subtract the original, and solve. That turns 0.333 recurring into 1/3 exactly. This calculator does not attempt it, because doing so would mean assuming a decimal you typed was meant to repeat.
- Decimal places
- How many digits after the point. Sets the denominator.
- GCD
- The greatest common divisor of the two parts. What you reduce by.
A worked example
The decimal 0.625.
That works out to 5/8 .
- Fraction
- 5/8
- Mixed number
- —
- Percentage
- 62.5000%
- Check
- 0.625000
Questions
How do I convert a decimal to a fraction?
Put the digits over one followed by as many zeros as there are decimal places, then reduce. 0.625 is 625/1000, which cancels down to 5/8.
What is 0.625 as a fraction?
Five eighths. It is 625/1000, and both parts divide by 125.
How do I convert a repeating decimal?
A different method: multiply by a power of ten, subtract the original and solve the result. That turns 0.333 recurring into exactly 1/3. This calculator treats what you type as terminating, so 0.333 comes back as 333/1000.
Which decimals are worth memorising?
0.5 is a half, 0.25 a quarter, 0.125 an eighth, 0.0625 a sixteenth, 0.2 a fifth and 0.75 three quarters. The halving sequence covers most measurements in inches.
Why is my fraction not simplified further?
Because it already is. If the numerator and denominator share no factor other than one, there is nothing left to cancel — 5/8 is finished, however unfamiliar it looks.
What about a decimal larger than one?
It works the same way and comes back as an improper fraction plus its mixed number form. 2.5 is 5/2, which is 2½.