Percent to Fraction Calculator

Percent ÷ 100 = fraction 37.5% → 37.5/100 → 375/1000 → 3/8

Percent

The number to convert, with or without its sign: 37.5, 50, 250, -25. Any finite value is accepted, and a value above a hundred is not a mistake.

Over a hundred

The first form, and the one the definition of a percentage gives directly: 37.5 percent is 37.5 hundredths, written 37.5/100. It is not a fraction yet, because the top is not a whole number.

Clearing the point

Multiply the top and the bottom by ten for every decimal place the percentage has, which is what turns 37.5/100 into 375/1000. The value is unchanged, since multiplying both parts of a fraction by the same number never changes it.

Lowest terms

The third form, with the common factors cancelled: 375/1000 and 50/100 both come down to smaller numbers. The panel prints the reduced form as its main answer and the form before reducing beside it, so the step can be followed rather than assumed.

Decimal

The same number as a plain decimal, printed to six places. It is the third spelling of the same quantity, useful when the fraction has to go into a spreadsheet or a formula.

Three uses are worth separating. The first is a percentage that has to be written as a fraction of whole numbers, which is what happens when a proportion is going into a recipe, a scale drawing or a gear ratio: 12.5 percent is 1/8, and eighths can be measured while 12.5 percent cannot. The second is simplifying: the panel does the reduction, so 50 percent comes back as 1/2 without the arithmetic being done on paper. The third is checking a fraction you already have against a percentage, where the unreduced form is the useful one, because it shows the hundred that the percentage came from before anything was cancelled.

1. 37.5 percent as a fraction

   1. Write it over a hundred: 37.5/100
   2. Clear the decimal point by multiplying both parts by ten: 375/1000
   3. Reduce by the common factor 125: 3/8

   The default case, and the one that shows why two forms are printed: the middle line is where the hundred and the tenth both become visible, and the last line is the answer.

2. 50 percent, where the two pages differ

   1. Write it over a hundred: 50/100
   2. There is no decimal point to clear, so this is already the form to reduce
   3. Reduce by fifty: 1/2

   Fifty percent is fifty hundredths, so 50/100 is the honest first form. The decimal to fraction converter, given 0.5 rather than 50 percent, would answer 5/10 instead, and both reduce to one half.

3. 250 percent, which is an improper fraction

   1. Write it over a hundred: 250/100
   2. Reduce by fifty: 5/2
   3. Read it back: five halves is two and a half, which is 250 percent

   An improper fraction is the right answer here and not a malformed one: a percentage above a hundred describes a quantity larger than its whole, and five halves is how that looks written as a fraction.

4. 0.0001 percent, at the floor of what the page can write

   1. Write it over a hundred: 0.0001/100
   2. Clear the point by multiplying both parts by ten thousand: 1/1000000
   3. Nothing cancels, so the two forms are the same

   A small percentage gives a large denominator, and here the form before reducing is already in lowest terms. Ten times smaller than this reads as zero, because the page works to twelve decimal places.

The percentage is read to twelve decimal places, so a value smaller than that is treated as zero rather than as a very small number, and the panel will print 0 for it. That is a limit of how far this page reads, not a fact about the number. The conversion is exact and never approximate: 0.3333 percent is 3333/10000, not 1/3, and anyone wanting one third should type 1/3 into a fraction calculator rather than expect this page to guess it. The form printed as the one before reducing depends on the page rather than only on the value, because the step being shown is the one this page performs: 50 percent reduces from 50/100 here, while the same half entered as 0.5 on the decimal to fraction page reduces from 5/10. Neither is wrong, and a figure copied between the two pages will look different in that one row. There is no upper bound on the percentage, so a very large one gives an improper fraction with a large numerator and the fraction is printed in full rather than as a mixed number.

How do I convert a percentage to a fraction?

Write it over a hundred, clear any decimal point by multiplying the top and bottom by ten for each decimal place, and reduce. Thirty seven and a half percent is 37.5/100, which becomes 375/1000, which reduces to 3/8.

Why is 50 percent shown as 50/100 rather than 5/10?

Because fifty percent means fifty hundredths, and the form before reducing shows the hundred that the percentage was defined against. The decimal to fraction page starts from a decimal instead of a percentage, so the same half entered there as 0.5 reduces from 5/10. Both give 1/2.

Does this page approximate at all?

No. The fraction is read off the decimal places that were typed, so 0.3333 percent becomes 3333/10000 and not 1/3. That matters when the fraction is going to be checked against the percentage later: an exact conversion can be turned back into the same percentage, while a guess cannot.

What if the percentage is more than a hundred?

The answer is an improper fraction, which is the correct form rather than a mistake: 250 percent is 5/2, and 150 percent is 3/2. A percentage above a hundred describes a quantity larger than its whole, and the fraction says so.

What is the second fraction on the panel for?

It is the form before reducing, which is the step between the percentage and the answer. Printing it turns the reduction into something that can be checked by eye: 375/1000 and 3/8 should be the same number, and the common factor that takes one to the other is 125.

Can the fraction be reduced further than the panel shows?

No. The main answer is in lowest terms, with every common factor cancelled, so there is no smaller pair of whole numbers with the same value. The unreduced form is deliberately not in lowest terms, and that is the whole point of printing it.

What happens with a very small percentage?

It gives a fraction with a large denominator rather than a rounded answer. One ten-thousandth of a percent is 1/1000000 exactly. Below twelve decimal places the percentage reads as zero, which is a limit of how far the page reads rather than a decision about the number.

• Reduced Fraction — a fraction written with the common factors of numerator and denominator cancelled, which is the last of the three steps on this page — Wolfram MathWorld (United States)
• Decimal fraction — an arithmetical fraction whose denominator is an integral power of ten, which is why clearing the decimal point means multiplying both parts by ten, a hundred or a thousand — Encyclopedia of Mathematics, European Mathematical Society (international)
• Percent — a ratio or fraction is converted to a percentage by multiplying by a hundred, so the reverse step is a division by a hundred and a fraction over a hundred is where every conversion on this page starts — Wolfram MathWorld (United States)