Fraction to Decimal Calculator
Convert a fraction to a decimal and a decimal back to a fraction. Detects repeating decimals and turns them into an exact fraction, fully simplified.
Decimal
0.625
Simplified fraction
5/8
A fraction in lowest terms terminates only when its denominator's prime factors are all 2s and 5s; otherwise the decimal repeats. Mark repeating digits with parentheses to convert them back to an exact fraction.
Frequently Asked Questions
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. If the division does not terminate, the decimal repeats, like 1/3 = 0.333… This calculator marks the repeating block for you.
How do I convert a decimal to a fraction?
Write the decimal over a power of ten matching its place value, then simplify. 0.25 = 25/100 = 1/4. For repeating decimals the calculator uses algebra to find the exact fraction instead of an approximation.
How do I turn a repeating decimal into a fraction?
Set the decimal equal to x, multiply by a power of ten to shift the repeating block, subtract to cancel the repeat, and solve. For example, 0.333… = 3/9 = 1/3, and 0.1666… = 1/6. Enter the digits and the calculator detects and converts the repeat.
Why do some fractions repeat and others don't?
A fraction in lowest terms gives a terminating decimal only when its denominator's prime factors are just 2s and 5s. Any other prime factor (like 3 or 7) forces the decimal to repeat forever.
What is the difference between a terminating and a repeating decimal?
A terminating decimal ends after a finite number of digits (0.75). A repeating decimal has one or more digits that cycle forever (0.272727…). Both are rational numbers and can be written as exact fractions.