This online Percent to Fraction Calculator converts a positive percentage to a fraction. In case the resulting fraction is an improper fraction (when the numerator is greater than the denominator) we present the result also in the form of a mixed number.
How to Convert Percent to Fraction
A percentage is a number or ratio expressed as a fraction of 100. It is actually just a special way of expressing a fraction with the denominator 100.
To convert a percent to a fraction, you first have to convert the percentage to a decimal just dividing the percentage by 100, and then convert the decimal to a fraction. For non repeating decimals the algorithm of conversion to a fraction is quite simple and is described in our Decimal To Fraction Converter.
So, the algorithm of conversion percentages to fractions used in this Percent to Fraction Calculator is as follows:
1) Divide a given percentage by 100 to get a decimal number. Let’s take 12.5% as an example. We have to convert this percentage to a decimal: 12.5% = 12.5 / 100 = 0.125.
2) Make a fraction with the decimal number as the numerator and write 1 as the denominator. Now, rewrite this number as a fraction: 0.125 = 0.125 / 1.
3) Multiply the numerator and denominator of this fraction by 10 until the decimal point in the numerator moves to the far right position. In our example we will have: 0.125 = 0.125 / 1 = 1.25 / 10 = 12.5 / 100 = 125 /1000.
4) Reduce the fraction dividing both the numerator and denominator by the greatest common divisor (GCD). In our example we can simplify the fraction, dividing the numerator and denominator by GCD = 125: 0.125 = 125 / 1000 = 1 / 8.
5) In case the numerator is greater than the denominator (the initial percentage is greater than 100%) you can further simplify the remaining fraction converting it to a mixed number. So, if we have initially 312.5%, we can convert it to the fraction 3.125, and then we could have 3.125 = 3125 / 1000 = 25 / 8 = 3 1/8. Or, even simpler, in view that 3.125 = 3 + 0.125 we can convert the fractional part only and have as the result: 3.125 = 3 + 0.125 = 3 + 1 / 8 = 3 1/8.
In case the resulting fraction is an improper fraction it’s also presented in the form of a mixed number. We use tiny Unicode characters to present the fractional part of the mixed number.
Related calculators
Check out our other percentage calculators such as Fraction to Percent Calculator and Percentage of a Percentage Calculator.