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Decimal to Fraction Calculator
Sign up to favourite this calculatorEnter a decimal to get it as an exact fraction in lowest terms. Repeating decimals are handled in full, with every step of the working shown.
0.125 as a fraction
Before simplifying
125/1000As a mixed number
N/A (Proper fraction)As a percentage
12.5%Decimal type
Terminating decimal- Start with
- x = 0.125
- Multiply by 1,000
- 1,000x = 125
- Write as a fraction
- x = 125/1000
- Divide both by 125
- x = 1/8
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Type the decimal, such as
0.125. Negatives and numbers above 1 both work. - If digits repeat, put them in brackets:
0.6(25)for 0.6252525…, or0.(3)for a third. - Read the fraction above the supporting figures, then open the working panel for the full derivation, line by line.
The working panel is the point of this tool rather than a footnote. Any calculator can print 1/8; the steps are what let you reproduce the conversion on paper, or check that a repeating decimal has been read the way you meant it.
Starting from a fraction instead? The Fraction to Decimal Calculator converts the other way.
What do I enter to convert a decimal?
- Decimal number — a whole number or decimal, positive or negative, such as
0.125or-2.5. It starts as 0.125. - Repeating digits — put the repeating block in brackets, so
0.6(25)means 0.6252525…. The closing bracket is required. - Length — up to 15 digits after the point, repeating digits included. Longer entries are rejected with a message.
What do the results show?
- As a fraction — the main answer, in lowest terms.
- Before simplifying — the fraction straight from the digits, before common factors are cancelled.
- As a mixed number — a whole part plus a fraction. It reads N/A for a proper fraction or a whole number.
- As a percentage — the same value multiplied by 100.
- Decimal type — whole number, terminating decimal, or repeating decimal and how many digits repeat.
- Working — the derivation line by line, ending with the step that reduces the fraction to lowest terms.
How to convert a decimal to a fraction
A terminating decimal is already a fraction with a power of ten underneath — the decimal point is just shorthand for it. Reducing that fraction is the only work left.
Fraction = Digits / 10places, then divide by the GCD
- Digits — the decimal with the point removed, e.g. 125
- places — how many digits followed the point, e.g. 3
- GCD — the greatest common divisor of top and bottom, e.g. 125
A repeating decimal needs one extra idea, because there is no last digit to put over a power of ten. Shift the number so the repeating block lines up with itself, then subtract:
(10p+q − 10p) × x = a whole number
- p — digits after the point before the repeat starts, e.g. 1 in 0.6(25)
- q — digits in the repeating block, e.g. 2 in 0.6(25)
- x — the number you are converting
For 0.6(25): 1000x = 625.2525… and 10x = 6.2525…. The tails are identical, so subtracting removes them entirely and leaves 990x = 619. Since 619 and 990 share no factor, 619/990 is already in lowest terms.
Worked examples
| Decimal | Before simplifying | In lowest terms |
|---|---|---|
| 0.5 | 5/10 | 1/2 |
| 0.125 | 125/1000 | 1/8 |
| 1.8 | 18/10 | 9/5 |
| 0.(3) | 3/9 | 1/3 |
| 1.8(3) | 165/90 | 11/6 |
| 0.6(25) | 619/990 | 619/990 |
The last row is the one that surprises people: 619/990 cannot be reduced at all, because 619 is prime. A messy-looking fraction is not a sign the conversion went wrong.
Frequently asked questions
How do I convert a decimal to a fraction?
Write the digits over the matching power of ten, then reduce. 0.125 has three decimal places, so it is 125/1000, and dividing both by their greatest common divisor of 125 gives 1/8. The calculator shows each of those steps.
How do I type a repeating decimal?
Put the repeating digits in brackets. 0.(3) means 0.3333…, 1.8(3) means 1.8333…, and 0.6(25) means 0.6252525…. Handwritten maths uses a line over the digits, which cannot be typed, so brackets stand in for it.
How does a repeating decimal become an exact fraction?
By subtracting the number from a shifted copy of itself, which cancels the infinite tail. If x = 0.6252525…, then 1000x = 625.2525… and 10x = 6.2525…; subtracting leaves 990x = 619, so x = 619/990 exactly. No rounding is involved anywhere.
Why do 1.8(3) and 1.8(33) give the same answer?
Because they are the same number written two ways: one marks a single repeating 3, the other a repeating pair of 3s, and both spell out 1.8333…. The algebra handles either notation and lands on 11/6 both times.
Can every decimal be written as a fraction?
Every terminating or repeating decimal can, which is what makes it a rational number. Decimals that never terminate and never repeat — pi, the square root of 2 — are irrational and have no exact fraction, only approximations such as 22/7.
What does the figure before simplifying mean?
It is the fraction straight from the digits, before the greatest common divisor is cancelled: 125/1000 for 0.125. It is worth seeing because it shows where the answer came from, and because the size of that divisor is the whole difference between 125/1000 and 1/8.
Last updated 25 October 2026.