Decimal to fraction calculator

Last updated 2026-10-02

This decimal to fraction calculator turns any decimal into a fraction in simplest form, and into a mixed number when it is bigger than 1. It handles repeating decimals too: put the repeating digits in parentheses, so $0.1\overline{6}$ is typed as 0.1(6).

This calculator needs JavaScript. Without it, the decimal to fraction chart lists the common decimals as fractions.

How to convert a terminating decimal to a fraction

Write it over a power of 10. Count the decimal places: one place is tenths, two is hundredths, three is thousandths. $0.375 = \frac{375}{1000}$ .
Find the greatest common factor of the top and bottom. For 375 and 1000 it is 125.
Divide both by it. $\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}$ .
Check it. Divide back: $3 \div 8 = 0.375$ .

How to convert a repeating decimal to a fraction

Call the decimal $x$ , multiply by a power of 10 that lines up the repeating part, and subtract so the endless tail cancels.

Example 1: 0.(3) as a fraction

Let $x = 0.333\ldots$
Multiply by 10, because one digit repeats: $10x = 3.333\ldots$
Subtract the first line from the second: $10x - x = 3.333\ldots - 0.333\ldots \quad\Rightarrow\quad 9x = 3$
Solve: $x = \frac{3}{9} = \frac{1}{3}$ .

So $0.\overline{3} = \frac{1}{3}$ . Check: $1 \div 3 = 0.333\ldots$

Example 2: 0.1(6) as a fraction

Let $x = 0.1666\ldots$ Only the 6 repeats, and it starts one place after the point.
$10x = 1.666\ldots$ and $100x = 16.666\ldots$
Subtract: $100x - 10x = 16.666\ldots - 1.666\ldots \quad\Rightarrow\quad 90x = 15$
Solve: $x = \frac{15}{90} = \frac{1}{6}$ .

So $0.1\overline{6} = \frac{1}{6}$ . Check: $1 \div 6 = 0.1666\ldots$

Common decimals as fractions

Decimal	Fraction
0.125	1/8
0.2	1/5
0.25	1/4
0.375	3/8
0.625	5/8
0.75	3/4

More rows are in the decimal to fraction chart, and the reverse conversion is in the fraction to decimal calculator.

Questions

How do I type a repeating decimal?

Put the repeating digits in parentheses: 0.(3) for one third, 0.1(6) for one sixth, 3.(142857) for twenty-two sevenths. If you type 0.333... the calculator assumes the last digit repeats and says so.

Does 0.999 repeating really equal 1?

Yes. With $x = 0.\overline{9}$ , $10x - x = 9$ , so $9x = 9$ and $x = 1$ . The calculator gives 1.

Can it convert negative decimals?

Yes. $-2.125$ becomes $-\frac{17}{8}$ , which is $-2\frac{1}{8}$ as a mixed number.

For a decimal inside a longer problem, photograph the problem in AI Math Tutor and follow each step to the answer.