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Decimal to Fraction Calculator

A decimal to fraction calculator turns any decimal into a simplified fraction in seconds. Type in a number like 0.75 and get 3/4, or 0.2 and get 1/5 — with the mixed-number form for values over 1 and a clear note whenever the result is an approximation of a repeating decimal. Switch to fraction-to-decimal mode to go the other way: enter a fraction like 1/3 and see its decimal, with the repeating digits marked.

Enter a decimal such as 0.75, 1.5, or 0.333. Repeating decimals are matched to the simplest fraction within 0.0005 of your number (denominator up to 1,000).

How it works

Every terminating decimal — one that ends, like 0.75 or 0.2 — is secretly a fraction with a denominator that is a power of 10. The number 0.75 means 75 hundredths, so it is 75/100. The number 0.2 means 2 tenths, so it is 2/10. The only work left is simplifying: divide the numerator and the denominator by their greatest common divisor until no number larger than 1 divides both. For 75/100, that divisor is 25, giving 3/4. For 2/10, it is 2, giving 1/5.

Repeating decimals need a different approach, because a number like 0.333... never ends and cannot be written exactly as a decimal at all. Its exact value is a fraction — 1/3 — and the way to find it is to look for the simple fraction closest to the decimal you typed. This calculator searches for the simplest fraction — the one with the smallest denominator — within 0.0005 of the decimal you typed, using denominators up to 1,000, then tells you honestly whether the match is exact or approximate and how far off it is. Typing 0.333 gives 1/3, which differs from 0.333 by only 0.000333, while typing 0.6667 gives 2/3. The stated tolerance is simple: the answer is the simplest fraction within 0.0005 of your decimal, and for ordinary decimals with a few digits it is exact.

Terminating decimal: 0.75 = 75/100 = 3/4 (divide top and bottom by 25)
0.2 = 2/10 = 1/5 (divide top and bottom by 2)
Repeating decimal: find the simplest fraction n/d (d ≤ 1,000) within 0.0005 of the decimal
Values over 1: 1.5 = 3/2 = 1 1/2

The fraction you get is always in lowest terms, which means the numerator and denominator share no common divisor bigger than 1. That matters because 75/100, 15/20, and 3/4 are all the same number, but 3/4 is the form people recognize and use. If the decimal is bigger than 1, the calculator also shows the mixed-number form: 1.5 is the improper fraction 3/2, which reads as 1 1/2, and 2.25 is 9/4, which reads as 2 1/4. Negative decimals work the same way, with the minus sign carried in front of the fraction.

Decimal-to-fraction conversion shows up in the kitchen, the workshop, and the classroom. A recipe written as 0.5 cups is easier to measure as 1/2 cup, and a ruler marked in fractions makes more sense of 0.375 inches when you see it is 3/8 of an inch. In woodworking, a cut of 0.25 inches is a quarter inch, and a board 1.75 inches thick is 1 3/4 inches. Fractions are also exact where decimals are not: a third of a cup is 1/3, while 0.33 cups is only an approximation that gets worse when you scale the recipe up.

Going the other way is just division: divide the numerator by the denominator. For 3/4, 3 ÷ 4 = 0.75 and the division ends, so the decimal terminates. For 1/3, the division never ends — 0.333... — because the remainder keeps coming back to 1. The calculator marks the repeating part in brackets, so 1/3 shows as 0.(3), 5/6 shows as 0.8(3), and 1/7 shows as 0.(142857). A fraction's decimal repeats exactly when its simplified denominator has a prime factor other than 2 or 5; otherwise it terminates.

Worked example

A baker in Seattle is doubling a recipe that calls for 0.75 cups of sugar per batch, and her measuring cups are marked in fractions. What fraction is 0.75?

Step 1 — write the decimal over a power of 10: 0.75 means 75 hundredths, so it is 75/100. Step 2 — find the greatest common divisor of 75 and 100, which is 25. Step 3 — divide the top and bottom by 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4, giving 3/4. Check: 3 ÷ 4 = 0.75, exactly right.

The same method works for 0.2: write it as 2/10, divide top and bottom by 2, and you get 1/5. Enter 0.75 in the calculator above and it returns 3/4; enter 0.2 and it returns 1/5.

FAQ

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For 3/4, 3 divided by 4 is 0.75, a terminating decimal. For 1/3, the division never ends and gives 0.333..., a repeating decimal, written as 0.(3) with the repeating digit in brackets. This calculator shows both forms, including the repeating part when there is one.

How do you convert 0.75 to a fraction?

Write 0.75 as 75/100, then divide the numerator and denominator by their greatest common divisor, 25. That gives 3/4. In general, write the decimal over a power of 10 and simplify: 0.2 becomes 2/10, which simplifies to 1/5.

What is 0.333... as a fraction?

0.333... (3 repeating forever) is exactly 1/3. No finite decimal equals it, so any decimal you type, like 0.333, is an approximation. This calculator matches repeating decimals to the simplest fraction within 0.0005 of the number you typed, using denominators up to 1,000, so 0.333 becomes 1/3, which differs from 0.333 by only 0.000333.

What is the difference between a terminating and a repeating decimal?

A terminating decimal ends, like 0.25 or 0.125, and converts to an exact fraction. A repeating decimal goes on forever with a repeating pattern, like 0.666... or 0.8333..., and its exact fraction has a denominator with a prime factor other than 2 or 5, such as 3. Repeating decimals can only be written exactly as fractions.

Can you convert a negative decimal to a fraction?

Yes. Convert the positive part to a fraction, then put the minus sign in front. For example, -0.4 becomes -(4/10) = -2/5. A decimal larger than 1, like 1.5, converts to an improper fraction, 3/2, which can also be written as the mixed number 1 1/2.

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