Decimal to Fraction Calculator

How it works

Write the decimal over a power of ten with as many zeros as there are decimal places, then simplify by dividing top and bottom by their greatest common divisor (GCD). Example: 0.375 = 375/1000; the GCD of 375 and 1000 is 125, so 0.375 = 3/8.

Repeating decimals cannot be written exactly with a finite number of digits, so 0.333 is 333/1000 exactly — but if the 3 repeats forever, the value is 1/3. The calculator shows both, using continued fractions to find the closest simple fraction.

What this decimal to fraction calculator shows

Type any decimal and the calculator returns the exact fraction in simplest form. Depending on the number, it also shows the mixed number (for values above 1), the percentage, and — for long or rounded decimals — the closest simple fraction, which is often the answer you actually want. If the last digits repeat (0.333, 0.6666), it also shows the fraction you get if that digit repeats forever.

It works for positive and negative numbers, numbers greater than one and decimals with up to nine digits after the point. Everything runs in your browser, so the answer appears instantly as you type, and you can copy the result with one click.

How to convert a decimal to a fraction, step by step

The method is the same for every decimal that ends (a terminating decimal). It has three steps:

1. Write the digits over a power of ten. Count the digits after the decimal point. One digit means tenths (over 10), two means hundredths (over 100), three means thousandths (over 1,000), and so on.
2. Find the greatest common divisor (GCD) of the top and bottom numbers — the largest number that divides both exactly.
3. Divide the numerator and denominator by the GCD. The result is the fraction in lowest terms.

For a slower, fully explained walk-through with practice questions, see how to convert a decimal to a fraction.

Why the denominator is a power of ten

Decimals are just fractions whose denominators are powers of ten, written in a shorter way. The position of each digit tells you its denominator, which is why the first step works:

So 0.43 literally means “43 hundredths”, or 43/100. Writing a decimal as a fraction is really just reading it out loud and writing down what you said — then tidying it up by simplifying.

Simplifying: finding the greatest common divisor

A fraction is in simplest form (lowest terms) when the numerator and denominator share no common factor other than 1. To get there quickly, divide both by their greatest common divisor rather than by small numbers one at a time.

Because the denominator is always a power of ten — made only of 2s and 5s — the GCD is also built only from 2s and 5s. That gives a handy shortcut: keep halving both numbers while they are even, then keep dividing by 5 while both end in 0 or 5. For example, 0.875: 875/1000 → divide by 5 → 175/200 → divide by 5 → 35/40 → divide by 5 → 7/8.

If you prefer the formal method, the Euclidean algorithm finds the GCD directly: divide the larger number by the smaller, replace the larger with the remainder, and repeat until the remainder is zero. The last non-zero remainder is the GCD. The calculator uses exactly this method.

Common decimals as fractions

These are the decimals people convert most often. Memorising the quarters and eighths makes everyday maths — recipes, measurements, discounts — much quicker.

For a complete printable table — every fraction from halves to tenths, plus 16ths, 32nds and 64ths — open the decimal to fraction chart.

Decimals greater than one: mixed numbers

For a decimal larger than 1, convert only the part after the point and keep the whole number in front. 2.75 becomes 2 and 75/100, which simplifies to 2 3/4. If you need an improper fraction instead (for multiplying or dividing fractions), multiply the whole number by the denominator and add the numerator: 2 3/4 = (2 × 4 + 3)/4 = 11/4.

Repeating decimals

Some fractions never end as decimals: 1/3 = 0.333…, 2/11 = 0.181818…, 1/7 = 0.142857142857…. If you type a rounded version such as 0.333, the calculator converts exactly what you typed (333/1000), but also shows 1/3 as the fraction for the repeating version.

For any repeating decimal, use the repeating decimal to fraction calculator, which lets you say exactly which digits repeat. The quick rule: put the repeating digits over the same number of 9s — 0.777… = 7/9 and 0.454545… = 45/99 = 5/11.

Rounded decimals and the closest simple fraction

Measurements and calculator results are often rounded, so the “exact” fraction of a rounded decimal can be ugly: 0.6667 is exactly 6667/10000, which is not useful. The calculator therefore also finds the closest simple fraction using continued fractions, a method that finds the best approximation for any limit on the denominator.

The maximum denominator controls how simple the answer is: 3.14159 becomes the famous 22/7 when the denominator is kept under 64. For tape measures and drill bits, the decimal to fraction inches calculator rounds to the nearest 1/8, 1/16, 1/32 or 1/64 inch and shows the error.

Decimal to fraction on a scientific calculator

Many scientific calculators can convert for you. On most Casio models, enter the decimal, press = and then the S⇔D key to switch between decimal and fraction form. On TI-84 graphing calculators, type the decimal, press MATH and choose ►Frac. Basic phone calculators and most spreadsheet defaults do not, which is where an online decimal to fraction converter is quicker.

In a spreadsheet you can format a cell as a fraction (for example “Up to two digits”), but it shows an approximation, not necessarily the exact value — check long decimals with the calculator above.

Which decimals terminate?

A fraction in lowest terms gives a terminating decimal only if its denominator has no prime factors other than 2 and 5. That is why eighths (8 = 2 × 2 × 2) and twentieths (20 = 2 × 2 × 5) end neatly, while thirds, sixths, sevenths, ninths and elevenths repeat forever. Turned around, every terminating decimal converts to a fraction whose denominator is built from 2s and 5s — a quick way to check an answer.

Common mistakes

• Using the wrong power of ten. 0.05 is 5/100, not 5/10. Count every digit after the point, including zeros.
• Stopping before the fraction is fully simplified. 25/100 reduces to 1/4, not 5/20.
• Treating a rounded decimal as a repeating one. 0.33 is 33/100; only 0.333… with the 3 repeating forever equals 1/3.
• Dropping the whole number. 3.5 is 3 1/2 (or 7/2), not 1/2.