Fraction to Decimal Converter: Exact Decimal Values

A fraction is a division waiting to happen: 3/4 means 3 divided by 4, which is 0.75. This converter performs that division for any fraction or mixed number and tells you whether the decimal terminates or repeats, so you always know exactly what kind of number you are dealing with.

Enter an optional whole number for mixed numbers like 2 and 3/4, which converts to 2.75. Negative fractions work too: -1/2 converts to -0.5. The simplified fraction is shown alongside, which is handy for homework that asks for both forms.

A fraction terminates when its simplified denominator has no prime factors other than 2 and 5: 1/2 is 0.5, 3/4 is 0.75, 7/20 is 0.35. Any other prime factor in the denominator makes the decimal repeat: 1/3 is 0.333..., 5/6 is 0.8333..., and 5/7 repeats a six-digit block.

Repeating decimals are shown with the repeating block in parentheses, like 0.(3) for 1/3, which is the standard compact notation. The decimal to fraction converter runs the reverse trip, turning decimals back into simplified fractions.

Example 1: 3/4. Divide 3 by 4 to get 0.75, a terminating decimal. Example 2: 2 and 1/3. The fraction part 1/3 repeats as 0.333..., so the mixed number is 2.333.... Example 3: 7/8. Divide 7 by 8 to get 0.875, which terminates because 8 is 2 cubed.

Example 4: -5/6. The sign carries through the division: -(5 / 6) = -0.8333.... Example 5: 22/7, the famous pi approximation, gives 3.142857 repeating, which is why it matches pi only to two decimal places.

Divide the numerator by the denominator with long division. For 5/8, 8 goes into 5.0 zero times, into 50 six times (48, remainder 2), into 20 two times (20, remainder 0), giving 0.625. When a remainder repeats a value you have seen before, the digits from that point repeat forever.

A shortcut for common fractions is worth memorizing: halves, quarters, and eighths all terminate, while thirds, sixths, and sevenths repeat. Knowing that 1/8 is 0.125 lets you build 3/8 as 0.375 and 5/8 as 0.625 by multiplication.

The most common mistake is flipping the fraction: 4/3 is 1.333..., not 0.75. Always divide the top number by the bottom number. The second is forgetting the whole number in a mixed number: 2 and 1/2 is 2.5, not 0.5.

A third mistake is rounding a repeating decimal too aggressively. Writing 1/3 as 0.33 introduces an error that grows when the value is multiplied later. Keep the repeating notation or several extra digits until the final step.

Fractions to decimals come up in recipes (half a cup is 0.5), construction (5/8 inch is 0.625), money (a quarter is 0.25), and test scores (17/20 is 85 percent). Spreadsheets and calculators want decimals, while people usually speak in fractions, so conversion bridges the two.

For fraction arithmetic without converting, the fraction calculator adds, subtracts, multiplies, and divides fractions directly, keeping everything in fraction form with the steps shown.