# Converting Between Fractions, Decimal Numbers and Percentages

Fractions and percentages are closely related—both express a part of a whole. Here, you will learn how to convert fractions and decimal numbers to percentages, and back.

Rule

### Percentage$\to$fraction$\to$decimalnumber

 $a\phantom{\rule{0.33em}{0ex}}\text{%}=\frac{a}{100}$

and to find the decimal number you simply calculate $a:100$.

In fact, you can change the percentage symbol to a regular number with the fraction $\frac{1}{100}$ in your calculations. Since we’re discussing parts in one hundred, you can write your percentage as a decimal number by using the tenths and hundredths place values. You can do it like this:

 $7\phantom{\rule{0.17em}{0ex}}\text{%}=7\cdot \frac{1}{100}=\frac{7}{100}=0.07$

Example 1

Write $\text{}20\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ both as a fraction and a decimal number.

 $20%=20\cdot \frac{1}{100}=\frac{20}{100}=\frac{20:20}{100:20}=\frac{1}{5}$
 $20%=20\cdot \frac{1}{100}=\frac{20}{100}=0,20=0,2$

Example 2

Write $\text{}65\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ both as a fraction and a decimal number.

 $65\phantom{\rule{0.17em}{0ex}}\text{%}=65\cdot \frac{1}{100}=\frac{65}{100}=\frac{65:5}{100:5}=\frac{13}{20}$
 $65\phantom{\rule{0.17em}{0ex}}\text{%}=65\cdot \frac{1}{100}=\frac{65}{100}=0.65$

Rule

### Fraction$\to$percentage

 $\frac{a}{100}=a\phantom{\rule{0.33em}{0ex}}\text{%}$

Rule

### Decimalnumber$d\to$percentage

 $d=d\cdot 100\phantom{\rule{0.17em}{0ex}}\text{%}$

You’re now going to learn how to go the other way, from fractions and decimal numbers to percentages. You can always change the fraction $\frac{1}{100}$ to a percentage symbol %. If you have more than $100$ %, your decimal number will be larger than $1$. Your goal is to make sure that your denominator is $100$. You will often have to expand or simplify your fraction.

Example 3

Write $\text{}0.25\text{}$ both as a fraction and a percentage.

 $0.25=\frac{25}{100}=\frac{25:25}{100:25}=\frac{1}{4}$
 $0.25=0.25\cdot 100\phantom{\rule{0.17em}{0ex}}\text{%}=25\phantom{\rule{0.17em}{0ex}}\text{%}$

Example 4

Write $\frac{1}{10}$ both as a decimal number and a percentage.

 $\frac{1}{10}=\frac{1\cdot 10}{10\cdot 10}=\frac{10}{100}=0.1$
 $\frac{1}{10}=\frac{1\cdot 10}{10\cdot 10}=\frac{10}{100}=10\cdot \frac{1}{100}=10\phantom{\rule{0.17em}{0ex}}\text{%}$

Example 5

Write $\text{}0.75\text{}$ both as a fraction and a percentage.

 $0.75=\frac{75}{100}=\frac{75:25}{100:25}=\frac{3}{4}$
 $0.75=75\cdot 100\phantom{\rule{0.17em}{0ex}}\text{%}=75\phantom{\rule{0.17em}{0ex}}\text{%}$