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Percent and growth factor

Percent means hundredths: $p\% = \frac{p}{100}$ . An increase of $p\%$ corresponds to multiplying by the growth factor $1+\frac{p}{100}$ , and a decrease corresponds to multiplying by $1-\frac{p}{100}$ . Several changes in a row are multiplied together.

p\% = \frac{p}{100}

percent as a decimal

\text{new} = \text{old}\cdot\left(1 \pm \frac{p}{100}\right)

growth factor for an increase (+) or decrease (−)

\text{change} = \frac{\text{new} - \text{old}}{\text{old}}\cdot 100\%

percentage change

Symbols

p

percentage rate

Example

A motor costs NOK 8000, the price is raised by 25% and then reduced by 20%:

$8000\cdot 1.25\cdot 0.80 = 8000$ NOK - the price is back where it started.

+20\%

followed by

-20\%

does not give the original price:

1.2\cdot 0.8 = 0.96

, i.e. 4% lower.

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Part of Foundations of Mathematics: Numbers, fractions and percent.