# Introduction

The word percent comes from the Latin word “cent” meaning “hundred”, such that “percent” means “per hundred”. Examples of percentages are:

• $1\%=\dfrac{1}{100}$
• $20\%=\dfrac{20}{100}$
• $60\%=\dfrac{60}{100}$
• $130\%=130/100=1+\dfrac{30}{100}$

The symbol % always means divided by 100.

# Converting a percentage to a fraction

So if we divide a whole into 100 equal parts, each part is 1 out of 100, or written as a fraction, 1/100. As a percent, this is 1%. This means that $1\%=\dfrac{1}{100}$

Therefore 45% of the whole will be 45/100.

Furthermore, 110% of the whole will be 110/100, which is more than a whole. We can write it as a mixed number $1\dfrac{10}{100}$

# Converting a fraction to a percentage

To convert a fraction to a percent, multiply by 100%.

For example, express 1/2 as a percentage, i.e.:

Another example, express 1/8 as a percentage, i.e.:

# Converting a percentage to a decimal

Percentages can be expressed as decimals.

For example, $1\%=\dfrac{1}{100}=0.01$

Alternatively, $45\%=\dfrac{45}{100}=0.45$

Alternatively, $200\%=\dfrac{200}{100}=2$. This is because there are 2 wholes, and not a proportion of one.

# Converting a decimal to a percentage

To convert a decimal to a percentage, multiply by 100%.

For example, $0.1=0.1*100\%=10\%$

Alternatively, $0.01=0.01*100\%=1\%$

In the further alternative, $2.01=2.01*100\%=201\%$