Percent to Fraction Conversion

Often times, you will be interested in different types of conversions when dealing with fraction, decimals and percents. Indeed, there is a natural connection between fractions and percentages.

For example, a fraction like a percentage of 25% is often understood as a "one quarter", which is obviously represented by the fraction "1/4". Now, there is obviously not just one fraction associated to 25%, as all the same as 1/4, we can write 25/100.

How do you convert a percent to fraction

The process involves two parts: one part is to convert the percent to a decimal, and then to convert the decimal into a fraction. For the first part, we use the formula

$$D = \displaystyle \frac{P}{100}$$

This formula shows how to get a decimal from the percent $P$, which is the number associated to the percent (without the % sign)

Steps for the conversion of a percent to fraction

1. Identify the percentage you want to convert, and call it $P$, after you remove the "%" sign
2. Compute the associated decimal $D$, using the formula $D = \displaystyle \frac{P}{100}$
3. Find the number of digits in the decimal part and call it $k$
4. The numerator of the fraction you are looking for is 10^k * D, and the denominator is 10^k

Examples: Converting percents to fractions

What is 0.38% as a fraction?

Solution: Following the steps outlined, first we identify the given percentage, which in this case is $P = 0.38\%$. Removing the "%" sign leads to the number $P = 0.38$. Then, we divide this number by 100:

$$D = \displaystyle \frac{P}{100} = \displaystyle \frac{0.38}{100} = 0.0038$$

So then, 0.38% corresponds to 0.0038. Now we convert it to a fraction. The number of digits is $k =4$, so we multiply 0.0038 by 10^4 = 10,000, as we get the fraction $\displaystyle \frac{38}{10000}$, which can be further simplified to $\displaystyle \frac{19}{5000}$

Useful calculators for decimals, fractions and percentages

If you are interest in the other way around, you can use this fraction to percent calculator, if instead you are provided with a fraction.

Very commonly used is this decimal to percent calculator, which allows you to convert between decimal and percentages.