Percent to Fraction Calculator

This calculator converts percentages to fractions. If the given value exceeds 100%, the calculator performs a percent to mixed number conversion.

Directions for use

To use this percent-to-fraction converter, enter the given percentage and press “Calculate.” The calculator will return the final answer and the detailed solution algorithm.

You can use integers and decimals as inputs. The initial percentage values can be positive or negative. Below are some examples of accepted inputs:

• 0.678
• -3.2
• 990
• 3e5

Fractions and numbers in scientific notation are not accepted. If you input a fraction or a number in scientific notation, the calculator will automatically disregard every symbol after the first fraction bar or multiplication sign. For example, if you enter \$\frac{3}{5}\$, the calculator will disregard everything after the fraction bar and perform the percentage-to-fraction conversion for the value of 3%, returning \$\frac{3}{100}\$ as the answer.

Similarly, if you input 6 × 10^2, the calculator will disregard every symbol after the multiplication sign and convert 6% to a fraction, returning \$\frac{3}{50}\$ as the answer.

Input values should not exceed 1,000,000. You can use commas to separate thousands in large input numbers, but it is unnecessary.

How to convert percent into a fraction

Let’s look at two algorithms for converting percentages into fractions.

Algorithm 1

To convert percent to fraction, perform the following steps:

1. Create the starting fraction by using the percentage value as the numerator and 100 as the denominator.
2. Check if the numerator is a whole number. If yes – proceed to step 4. If no – perform step 3 first.
3. If the numerator is a decimal, count the number of digits after the decimal point. Let’s say you have n digits after the decimal point. Multiply both the numerator and the denominator by 10ⁿ.
4. Simplify the resulting fraction.

Example 1

Convert 5% into a fraction. Following the above algorithm, we get:

1. Creating the starting fraction with 5 as the numerator and 100 as the denominator, we get \$\frac{5}{100}\$.
2. 5 is a whole number. Therefore, we can proceed to step 4.
3. Simplifying \$\frac{5}{100}\$, we get:

\$\frac{5}{100}\$ = \$\frac{1}{20}\$

Example 2

Convert 60.25% into a fraction. Following the above algorithm, we get:

1. The starting fraction is \$\frac{60.25}{100}\$.
2. 60.25 is not a whole number. Therefore, we go to step 3.
3. The number of digits after the decimal point, n, is 2: n = 2. Multiplying both the numerator and the denominator by 10ⁿ = 10² = 100, we get \$\frac{6025}{10000}\$.
4. Simplifying

$$\frac{6025}{10000}$$,

we get:

$$\frac{6025}{10000} = \frac{\frac{6025}{25}}{\frac{10000}{25}} = \frac{241}{400}$$

Algorithm 2

The idea behind the second algorithm is the same since we need to perform equivalent mathematical operations to get the same answer, regardless of which solution algorithm we choose. The choice of an algorithm is a question of personal preference. The calculator on this page uses (and demonstrates) Algorithm 2. To use this algorithm, follow the steps below:

1. Convert the given percentage value to a decimal by dividing it by 100. This step is equivalent to moving the decimal point two positions to the left.
2. Create the starting fraction by using the decimal from step 1 as the numerator and 1 as the denominator.
3. Follow steps 2 – 4 from the previous algorithm.

Example 3

Convert 40% into a fraction.

Let’s use Algorithm 2 for this conversion:

1. \$\frac{40}{100}\$ = 0.4. Note how dividing 40 by 100 is equivalent to moving the decimal point two positions to the left: the original value is a whole number. Therefore, the decimal point would have initially been after the final digit of the number: 40 = 40.0.
2. The starting function will have 0.4 as the numerator and 100 as the denominator: \$\frac{0.4}{1}\$.
3. 0.4 is not a whole number. Therefore, we need to count the number of digits after the decimal point: n = 1. Now we multiply the starting fraction's numerator and denominator by 10ⁿ = 10¹ = 10:

\$\frac{0.4}{1}\$ = \$\frac{4}{10}\$

4. Simplifying, we get:

\$\frac{4}{10}\$ = \$\frac{2}{5}\$

Converting percentages to mixed numbers

The algorithm of converting percentages into mixed numbers is the same as that of converting percentages into fractions, with the final simplification step also including improper fraction to mixed number conversion. A percentage is converted into a mixed number if the initial percentage value is larger than 100%.

Example 4

Convert 125% to a mixed number.

Let’s follow Algorithm 2:

1. \$\frac{125}{100}\$ = 1.25
2. The starting fraction will be: \$\frac{1.25}{1}\$
3. 1.25 is not a whole number. Therefore, we need to count the number of digits after the decimal point: n = 2. Multiplying the numerator and the denominator of the starting fraction by 10ⁿ = 10² = 100, we get:

\$\frac{1.25}{1}\$ = \$\frac{125}{100}\$

4. \$\frac{125}{100}\$ = \$\frac{5}{4}\$ = \$1\frac{1}{4}\$

Real-life applications

Percentages are fractions that always have 100 in the denominator. 1% is a hundredth part of a whole: 1% = \$\frac{1}{100}\$. Converting percentages to fractions is very useful for performing mathematical calculations with percentages.

Example 5

Alice is in a store buying a pair of shoes with a 25% discount. If the original price of the shoe was $300, what is the new price?

Solution

We first need to calculate the dollar equivalent of the 25% discount to find out the new price. To do that, let’s convert 25% to a fraction, following Algorithm 2:

1. \$\frac{25}{100}\$ = 0.25
2. The starting fraction will be \$\frac{0.25}{1}\$
3. 0.25 is not a whole number. Therefore, we need to count the number of digits after the decimal point: n = 2. Multiplying the numerator and the denominator of the starting fraction by 10ⁿ = 10² = 100, we get:

\$\frac{0.25}{1}\$ = \$\frac{25}{100}\$

4. Simplifying, we get:

\$\frac{25}{100}\$ = \$\frac{1}{4}\$

Since 25% = \$\frac{1}{4}\$, to find the discount in dollars, we have to divide the original price by 4:

\$\frac{300}{4}\$ = 75

The new price will be 300 – 75 = 225.

Answer

The new price of the shoes is $225.