7 Percentages

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\%

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