Percent To Fraction And Decimal Numbers

Percent and fractions are usually used in our daily life to relate and compare quantity. For example we use percentage or percent to rank in class, comparing marks and performance. In simple words, the percent is a way of expression a fraction of 100 by number.

Percent refers to the fractions of a whole and can be remembered easily than the fraction. It is how much of a whole thing contains. For example, \( \small 50 \% \) can be written as \( \small \frac{1}{2} \), and \( \small 25 \% \) means \( \small \frac{1}{4} \). In the same way you can convert vice versa: fraction to percent conversion.

You often need to find out what percent of something in your daily life. To understand how to convert percent to fraction, consider an example. If a school has 865 students out of which 389 are female, then what percent of students are female. To solve this you need to divide both the numbers. It is 389 out of 865 or \( \small \frac{389}{865} = 0.44971 \). To simplify this you need to convert it into percent, which is \( \small 44.9711 \% \). Now, let’s discuss how to convert percent and fraction in detail.

What is a Percent?

In a simple word, percentage actually means “out of a hundred”. The word is derived from Latin word – percentumfor which means thoroughly hundred. It is number that is being used to express a fraction of 100. It is denoted by a sign \(\small \left ( \% \right )\) called percentage. In this sense, \( \small 64 \% \) can be written in a fraction as \( \small \frac{64}{100} \). Another example, in a school \( \small 80 \% \) of students are female, which means out of 100 students 80 are female.

What is a Fraction?

Fraction is a number of part of a whole thing. It represents how many part of a certain size is divided into a whole thing. A fraction consists of a numerator and a denominator: \( \small \frac{1}{2} \), where the number which is written above the line is called as numerator, and the denominator is written below the line.

The numerator represents a number of parts of a whole thing, while the denominator indicates how many parts makes up a whole thing, which can’t be a zero. For instance, an apple is equally sliced into four pieces and you are using only three pieces, then as a fraction it can be written as \( \small \frac{3}{4} \), here, the numerator: 3 represents parts of the apple and the denominator: 4 indicates there are four equal parts of the apple.

How to Convert Percent to Fraction

Percent to fraction conversion is very simple using the formula provided in this page. As you already know that percent means “out of a hundred.” You first need to convert a percent a decimal and then convert the decimal to fraction. You can also use Byju’s Online Percent Calculator to convert a fraction to percent. However, below are few examples and a conversation table that will help you to get the percent and fraction instantly.

Steps to Convert Percent to Fraction

Method One

Step 1: Divide the given percent by 100. This will give a decimal number.

Step 2: Count number of digits after a decimal point. The digit is represented as \( \small d \).

The decimal number 2.56 has two digits after the decimal point, so \(\small d = 2\).

Step 3: Now, calculate the factor \(\small (f)\). This will convert the decimal number as an integer using a formula \(\small f = 10^{d}\)

\(\small f = 10^{2} = 100\)

Step 4: The decimal number should be multiplied and divided by the factor

\( \small \frac{2.56 \times 100}{100} = \frac{256}{100} \)

Step 5: Find Greatest Common Divisor (GCD) of the fraction: \( \small \frac{256}{100} \)

GCD \(\small (256, 100) = 4\)

Step 6: Simply the fraction by dividing the numerator and denominator by the GCD value:

\(\frac{256}{100} = \frac{\left ( \frac{256}{4} \right )}{\left ( \frac{100}{4}\right )} = \frac{64}{25}\)

Method Two

Step 1: Divide the given percent by 100 to get the decimal number \( \frac{percent}{100} \).

Step 2: If the percent is not a whole number, then multiply every number by 10 after the decimal point.

Step 3: Simplify the fraction.

Percent to Fraction Conversion Table

Percent Fraction
\( 1 \% \) \( \frac{1}{100}\)
\( 10 \% \) \( \frac{1}{10} \)
\( 11.11 \% \) \( \frac{1}{9} \)
\( 12.5 \% \) \( \frac{1}{8} \)
\( 14.29 \% \) \( \frac{1}{7} \)
\( 16.67 \% \) \( \frac{1}{6} \)
\( 20 \% \) \( \frac{1}{5} \)
\( 22.22 \% \) \( \frac{2}{9} \)
\( 25 \% \) \( \frac{1}{4} \)
\( 28.57 \% \) \( \frac{2}{7} \)
\( 30 \% \) \( \frac{3}{7} \)
\( 33.33 \% \) \( \frac{1}{3} \)
\( 37.5 \% \) \( \frac{3}{8} \)
\( 40 \% \) \( \frac{2}{5} \)
\( 42.86 \% \) \( \frac{3}{7} \)
\( 44.44 \% \) \( \frac{4}{9} \)
\( 50 \% \) \( \frac{1}{2} \)
\( 55.56 \% \) \( \frac{5}{9} \)
\( 57.17 \% \) \( \frac{4}{7} \)
\( 62.5 \% \) \( \frac{5}{8} \)
\( 66.67 \% \) \( \frac{2}{3} \)
\( 60 \% \) \( \frac{3}{5} \)
\( 70 \% \) \( \frac{7}{10} \)
\( 71.43 \% \) \( \frac{5}{7} \)
\( 75 \% \) \( \frac{3}{4} \)
\( 77.78 \% \) \( \frac{7}{9} \)
\( 80 \% \) \( \frac{4}{5} \)
\( 83.33 \% \) \( \frac{5}{6} \)
\( 85.71 \% \) \( \frac{6}{7} \)
\( 87.5 \% \) \(  \frac{7}{8} \)
\( 88.89 \) \(  \frac{8}{9} \)
\( 90 \% \) \( \frac{9}{10} \)

Percent to Fraction Examples

Example 1: Convert \( \small 11 \% \) to fraction.

Solution:

Step 1: Divide the percent by 100 to get the decimal number.

\( \small \frac{11}{100} \)

Step 2: The given percent is a whole number, so go to step 3.

Step 3: The fraction \( \small \frac{11}{100} \) can’t be simplified further

The answer is \( \small \frac{11}{100} \).

Example 2: Convert \( \small 75 \% \)  to a fraction.

Solution:

Step 1: Divide the percent by 100 to get the decimal number.

\( \small \frac{75}{100} \)

Step 2: The given percent is a whole number, so go to step 3.

Step 3: Simply the fraction \( \small \frac{75}{100} \).

The answer is \( \small \frac{3}{4} \).

Example 3: Convert \( \small 62.5 \% \)  to a fraction.

Solution:

Step 1: Write down the given percent as: \( \small \frac{62.5 }{100} \)

Step 2: The given percent is not a whole number, so multiply both the numerator and denominator by 10, because there is one digit after the decimal point.

Step 3: \( \small \frac{62.5 \times 10}{100 \times 10} \)

\( \small = \frac{625}{1000} \)

Step 4: Simply the fraction: \( \small = \frac{625}{1000} \)

The answer is \( \small \frac{5}{8} \)..


Practise This Question

Which of the following is an irrational number? 

i) 23

ii) 0.143¯¯¯¯¯¯32

iii) 5.¯¯¯¯¯¯46

iv) 5