Decimal to Fraction Calculator — convert a decimal to a fraction

How it works

A terminating decimal is just a fraction whose denominator is a power of ten. Reading the decimal places tells you which power: one place is tenths, two places hundredths, three places thousandths, and so on. Write the digits over that power of ten, then reduce the fraction to lowest terms.

For 0.75, there are two decimal places, so it is 75/100. The greatest common divisor of 75 and 100 is 25, and dividing both by 25 gives 3/4. A fraction, per Wolfram MathWorld, is simply a rational number written as a numerator over a denominator — which is exactly what a terminating decimal is.

If the decimal is larger than 1, the calculator also gives a mixed number: 2.75 is 11/4 as an improper fraction, or 2 3/4 as a whole number plus a proper fraction. The calculator finds the simplest fraction that equals your decimal, so common values like 0.333… return 1/3 rather than a long, unwieldy fraction.

Worked example

Take 0.75. It has two decimal places, so write it as 75/100. Divide the top and bottom by their greatest common divisor, 25, to get 3/4. Since 0.75 is less than 1, the mixed number is just 3/4 as well. For 2.75, the same process gives 11/4, or 2 3/4.

Frequently asked questions

How do you convert a decimal to a fraction?

Write the decimal's digits over the matching power of ten — tenths for one place, hundredths for two, and so on — then reduce to lowest terms. For example, 0.75 is 75/100, which simplifies to 3/4.

What is 0.75 as a fraction?

0.75 equals 3/4. It is 75/100, and dividing both numbers by their greatest common divisor (25) gives 3/4.

How do I convert a decimal bigger than 1?

Convert it the same way to get an improper fraction, then optionally split off the whole part for a mixed number. For instance, 2.75 is 11/4, which is 2 3/4.

Can every decimal be written as a fraction?

Every terminating or repeating decimal is a rational number and can be written as an exact fraction. This calculator finds the simplest fraction matching your decimal, so 0.333… returns 1/3.

What is 0.125 as a fraction?

0.125 is 1/8. It equals 125/1000, and dividing top and bottom by their greatest common divisor (125) gives 1/8.

How are negative decimals handled?

The sign stays with the fraction: −0.75 becomes −3/4, and −2.75 becomes −2 3/4. The size of the fraction is found first, then the negative sign is applied.