Fraction to Decimal Converter
Convert fractions into decimal values.
Converting fractions to decimals
A fraction is a division waiting to happen: the line between numerator and denominator means 'divided by'. Converting to a decimal is therefore just carrying out that division. This converter handles proper fractions, improper fractions and the recurring decimals that certain denominators always produce.
How to use the Fraction to Decimal Converter
- Type the Fraction in the form
7/8. - The decimal appears immediately.
- Improper fractions such as
9/4work too. - Watch for recurring results — thirds and sevenths never terminate.
Formula and a worked example
Decimal = numerator ÷ denominator
A fraction gives a terminating decimal only when its denominator, in lowest terms, has no prime factors other than 2 and 5. That is why halves, quarters, fifths and eighths are tidy while thirds, sixths and sevenths recur forever.
Worked example
7/8 = 0.875 exactly, because 8 is 2³. But 1/3 = 0.3333… and 1/7 = 0.142857142857…, repeating in a six-digit cycle, because 3 and 7 are neither 2 nor 5.
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the top number by the bottom number. 3/4 is 3 ÷ 4 = 0.75.
How do I convert a decimal back to a fraction?
Write the decimal over a power of ten, then simplify. 0.375 is 375/1000, which reduces to 3/8.
Which fractions give recurring decimals?
Any whose simplified denominator has a prime factor other than 2 or 5 — thirds, sixths, sevenths, ninths and so on.
How do I turn a fraction into a percentage?
Convert to a decimal, then multiply by 100. 7/8 = 0.875 = 87.5%.
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