Percentage change

Description

Percentage change measures how much a value has increased or decreased, expressed as a percentage of the original value.

$$\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100$$

Percentage increase example: original price £80, new price £92. $$\text{Change} = 92 - 80 = 12, \quad \frac{12}{80} \times 100 = 15%\text{ increase}$$

Percentage decrease example: a plant was 45 cm, now 36 cm. $$\frac{45 - 36}{45} \times 100 = \frac{9}{45} \times 100 = 20%\text{ decrease}$$

Multiplier method: to increase by $r%$, multiply by $\left(1 + \frac{r}{100}\right)$; to decrease, multiply by $\left(1 - \frac{r}{100}\right)$.

• Increase by 15%: $\times 1.15$
• Decrease by 20%: $\times 0.80$

Common error: dividing by the new value instead of the original value when calculating percentage change.

Links

Reverse percentages Compound growth & decay