Percent, Decimal and Fraction Converter

Convert percent to decimal, decimal to fraction, fraction to percent — any of the three into the other two, exactly, with the fraction in simplest form, mixed numbers and repeating decimals such as 0.333… shown as they really are.

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How do you convert a percent to a decimal?

Divide it by 100, which moves the decimal point two places to the left: 37.5% is 0.375 and 5% is 0.05. For the fraction, write the decimal over a power of ten and simplify by the greatest common divisor, so 0.375 = 375/1000 = 3/8.

Cost: Free, no limits
Upload: None — runs on your device
Sign-up: Not required
Works offline: Yes, once loaded

How to convert a percent to a decimal or fraction

Choose what you are converting from
Pick Percent, Decimal or Fraction. Each tab keeps its own value, so you can switch back and forth.
Type the value
Enter 37.5%, 0.375 or 3/8. A mixed number goes in as 1 3/4, and a repeating decimal as 0.(3) or 0.333….
Read the other forms
The percent, decimal and simplest fraction appear at once, plus a mixed number when the value is above 1. Each has its own Copy button.

Examples

37.5%0.375 · 3/8
The percentage over 100, simplified by dividing top and bottom by 125.
1/60.1(6) · 16.(6)% · rounded 0.1666666667
Six has a factor of 3, so the decimal repeats.
1 3/41.75 · 175% · 7/4
A mixed number, converted through the improper fraction.

Key features of the Percent, Decimal and Fraction Converter

Percent, decimal and fraction, converted in any direction
Fractions reduced to simplest form by greatest common divisor
Repeating decimals shown exactly, with the repeating block in brackets
Mixed numbers in and out, including negative values
Exact arithmetic on whole numbers, with no floating-point rounding errors
A hint when a rounded decimal such as 0.333 is probably a simple fraction

What it converts

Input

Percent (37.5 or 37.5%)
Decimal (0.375)
Repeating decimal (0.(3) or 0.333…)
Fraction (3/8)
Mixed number (1 3/4)

Output

Percent
Decimal, exact
Decimal rounded to 10 places when it repeats
Simplest fraction
Mixed number

When should you use this?

Turning a percentage from a report or exam question into a fraction or decimal.
Checking homework that asks for a fraction in simplest form or as a mixed number.
Converting a measurement or recipe quantity such as 0.375 into 3/8.

Limitations

Input is limited to 40 characters, which covers far more precision than everyday numbers need.
A plain decimal is converted exactly as typed: 0.333 is 333/1000. Only a decimal written with brackets or a trailing ellipsis is treated as repeating.
When a repeating block is longer than 200 digits it is cut off and marked with …; the fraction is still exact.
Fractions must use whole numbers on top and bottom — 1.5/2 is not accepted; enter 0.75 in the Decimal tab instead.

Troubleshooting

It says the value looks like a fraction or has a % sign

Each tab reads one form. Switch to the Fraction tab for 3/8, or the Percent tab for 37.5%, or remove the symbol.

0.6667… gives 2/3 but 0.6667 gives 6667/10000

That is intended: the ellipsis says the decimal continues, so the simplest nearby fraction is used. Without it the number is taken exactly as typed.

Common mistakes to avoid

Moving the decimal point the wrong way. Percent to decimal divides by 100 (37.5% → 0.375); decimal to percent multiplies by 100.
Treating 0.33 as one third. It is 33/100; one third is 0.333… forever, and the difference matters in anything multiplied up.
Writing a mixed number without a space. 13/4 is thirteen quarters, while 1 3/4 is one and three quarters.

Pro tips

Tips for better results

Mental maths
Learn the eighths and most fractions follow
To check a fraction quickly in your head, learn the eighths: 1/8 = 0.125, so 3/8 = 0.375, 5/8 = 0.625 and 7/8 = 0.875.
Rounded results
Add an ellipsis to recover the fraction behind a rounded decimal
If a decimal is a rounded calculator result, type it with a trailing … so the converter looks for the simple fraction it came from.
Terminating
Only 2s and 5s in the denominator give a decimal that ends
A fraction whose bottom number has only 2s and 5s as factors always gives a decimal that ends; anything else repeats.

How the three forms relate

A percentage is a number of hundredths, so 37.5% is 37.5 ÷ 100 = 0.375. A decimal becomes a fraction by writing its digits over the matching power of ten — 0.375 is 375/1000 — and dividing the top and bottom by their greatest common divisor, here 125, which leaves 3/8. Going the other way, a fraction becomes a decimal by dividing the top number by the bottom one.

This converter does all of that with exact whole-number arithmetic rather than floating point, so 0.1 stays 1/10 and never turns into 0.1000000000000000055, which is what a computer's ordinary number type actually stores.

Repeating decimals

A fraction in lowest terms has a decimal that ends only when its bottom number has no prime factors other than 2 and 5. Every other fraction repeats forever: 1/3 is 0.333…, 1/6 is 0.1666…, 1/7 is 0.142857142857…. The result shows the repeating block in brackets — 0.(3), 0.1(6), 0.(142857) — and a rounded version beside it for copying into something that needs a plain number.

You can type repeating decimals the same way. 0.(3) is read as exactly one third. A value ending in an ellipsis, such as 0.1666…, is read as repeating when its last digit or block of up to six digits appears twice in a row (or when only one digit follows the point); otherwise the converter takes the simplest fraction within one unit of the last digit you typed, which is how 0.6667… becomes 2/3.

Percentages over 100 and below zero

Nothing stops a percentage going past 100: 150% is 1.5, or 3/2, or the mixed number 1 1/2. Negative values convert the same way with the sign kept, so -25% is -0.25 and -1/4. To work out a percentage of an amount rather than convert between forms, use the percentage calculator.

Privacy

The Percent, Decimal and Fraction Converter runs entirely in your browser. What you enter and the result it produces stay on your own device — nothing is sent anywhere, because nothing needs to be.

You can confirm this rather than take our word for it: open your browser’s developer tools, watch the Network tab, and use the tool. No request carries your input. It also keeps working with the connection off.

Details are in the privacy policy.

What next?

For X% of Y, or percentage change.

Work out a percentage of a number

Percent, Decimal and Fraction Converter — questions

How do I convert a percent to a fraction?

Write the percentage over 100 and simplify. 37.5% is 37.5/100, which is 375/1000 once the decimal point is cleared, and dividing both by 125 gives 3/8. The converter does the simplifying for you with the greatest common divisor.

How do I convert a decimal to a fraction?

Put the digits after the point over 10, 100, 1000 and so on — one zero per decimal place — then simplify. 0.45 is 45/100, which reduces to 9/20. A repeating decimal needs a different method; type it as 0.(3) or 0.333… and the converter works it out.

Why does 0.333 give 333/1000 rather than 1/3?

Because 0.333 is exactly 333/1000; one third is 0.333 repeating forever. When a decimal of three or more places is close to a simple fraction with a bottom number up to 20, the result says so — 0.333 shows the hint 1/3. Type 0.333… or 0.(3) to mean one third exactly.

What is a mixed number?

A whole number and a proper fraction written together, such as 1 3/4 for seven quarters. The converter shows one whenever the value is more than 1 and not whole, and accepts one as input if you put a space between the whole number and the fraction.

How do you convert to decimal from a fraction?

Divide the top number by the bottom number: 3/8 is 3 ÷ 8 = 0.375. If the division never ends, the digits fall into a repeating block, which the converter shows in brackets — 2/3 is 0.(6).

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