Decimal to fraction converter
Convert any decimal number to a fraction in lowest terms with full working shown.
How to convert a decimal to a fraction
To convert a decimal to a fraction, count the number of decimal places. Write the digits after the decimal point as the numerator, and a power of 10 as the denominator (10 for one decimal place, 100 for two, 1000 for three). Then simplify by dividing both by their GCF.
Example: 0.375
Three decimal places → write as 375/1000. GCF(375, 1000) = 125. Divide both: 375÷125 = 3, 1000÷125 = 8. So 0.375 = 3/8.
Example: 0.5
One decimal place → write as 5/10. GCF(5, 10) = 5. Divide both: 5÷5 = 1, 10÷5 = 2. So 0.5 = 1/2.
Repeating decimals
For repeating decimals like 0.333... (0.3̄), set x = 0.333..., multiply by 10: 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3.
Frequently asked questions
Can every decimal be written as a fraction?
Every terminating decimal (like 0.25) and every repeating decimal (like 0.333...) can be written as a fraction. Non-repeating, non-terminating decimals like π cannot.
How do I know if a fraction will be a terminating decimal?
A fraction a/b in lowest terms gives a terminating decimal if and only if the denominator b has no prime factors other than 2 and 5.