How to convert a decimal to a fraction
To turn a decimal into a fraction, write the digits over the matching power of 10, then simplify. For 0.75, write 75/100, then divide top and bottom by their greatest common divisor (25) to get 3/4.
The power of 10 is chosen by counting decimal places: one place means a denominator of 10, two places 100, three places 1000, and so on. That is why 0.75, with two decimal places, starts life as 75/100 before any reducing happens. Going the other direction is just a division, handled by the fraction to decimal calculator.
Reducing to lowest terms
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. This calculator finds the greatest common divisor and divides both parts by it automatically. Prime factors help here — see the prime factorization calculator.
Reducing never changes the value, only how it is written: 75/100, 15/20 and 3/4 are the same number. Because every power of 10 factors into 2s and 5s, a terminating decimal always reduces to a fraction whose denominator contains only 2s and 5s. If your answer keeps a denominator with a 3 or a 7 in it, the original decimal was not a clean terminating one.
How to use this calculator
Enter a decimal value, such as 0.75 or 1.2. The tool returns the equivalent fraction in simplest form, including negatives. Terminating decimals convert exactly; long repeating decimals are approximated by their entered digits.
Values greater than 1 come back as improper fractions — 1.2 becomes 6/5 rather than the mixed number 1 1/5 — and whole numbers come back with no denominator at all. Trailing zeros are harmless: 0.750 and 0.75 both reduce to 3/4, because the extra zero cancels during the reduction step. The result is not always in lowest terms, so finish with the fraction simplifier.
Frequently asked questions
- What is 0.75 as a fraction?
- 0.75 equals 3/4. Written as 75/100 and reduced by dividing both by 25.
- How does the conversion work?
- The decimal is placed over a power of 10, then both numbers are divided by their greatest common divisor.
- Does it handle negative decimals?
- Yes. A negative decimal converts to a negative fraction in lowest terms.
- What about repeating decimals?
- Repeating decimals are approximated using the digits you enter, so the fraction matches those digits.
- Why does 0.333 not come back as 1/3?
- Because 0.333 and 1/3 are different numbers — 1/3 is 0.3333… repeating forever. The tool converts exactly the digits you type, giving 333/1000. To get 1/3 you need the algebraic trick for repeating decimals, not a power-of-ten denominator.