Decimal to Fraction Calculator

Decimal to fraction at a glance#

A decimal to fraction calculator rewrites a decimal as a fraction in its simplest form. Write the decimal over a power of 10 set by its decimal places, then divide the top and bottom by their greatest common factor. So 0.75 is 75/100, which reduces to 3/4.

Count the digits after the point to pick the power of 10: one digit means tenths, two means hundredths, three means thousandths. For 0.125 that is three places, so the raw fraction is 125/1000, and dividing both parts by 125 gives 1/8. A repeating decimal such as 0.666... is handled differently and resolves to 2/3.

Enter your decimal in the calculator above for the exact fraction and its reduced form. Results round at the precision you set, so a long repeating decimal is shown to a fixed number of places.

How to convert a decimal to a fraction#

Write the decimal over a power of 10 set by its decimal places, then reduce. Count the digits after the point: one digit is tenths, two is hundredths, three is thousandths. So 0.005 has three places and becomes 5/1000, which divides by 5 to give 1/200.

Decimals greater than one#

Keep the whole-number part aside and convert only the part after the point. For 2.25, the 0.25 becomes 25/100, which reduces to 1/4, so 2.25 is 2 1/4. As a single improper fraction that is 9/4.

Converting repeating decimals#

A repeating decimal needs algebra, not a power of 10. Set the decimal equal to x, multiply by 10 for each repeating digit, then subtract to cancel the tail. For 2.666..., let x = 2.666... and 10x = 26.666...; subtracting gives 9x = 24, so x = 24/9 = 8/3, which is 2 2/3.

Frequently asked questions#

What is 0.75 as a fraction?#

0.75 is 75/100, and dividing both numbers by 25 gives 3/4. Two decimal places means hundredths, so the raw fraction sits over 100.

How do I convert a repeating decimal to a fraction?#

Use algebra: set x to the decimal, multiply by 10 per repeating digit, subtract the original, then solve. 0.666... gives 9x = 6, so x = 6/9 = 2/3.

How does the calculator simplify the fraction?#

It divides the numerator and denominator by their greatest common factor until they share no factor but 1. That reduces 75/100 to 3/4 in one step.

Why does the result depend on decimal places?#

The number of decimal places sets the power of 10 you divide by. One place is over 10, two places over 100, three over 1000, before any reduction.

Can every decimal become a fraction?#

Every terminating or repeating decimal converts to an exact fraction. Non-repeating, non-ending decimals such as pi cannot, so they are only approximated.