8.5Percentage Change

Percentage change measures how much a quantity has increased or decreased relative to its original value.

Percentage change

\displaystyle \text{Percentage change} = \dfrac{\text{New value} - \text{Original value}}{\text{Original value}} \times 100\%

A positive result is a percentage increase.
A negative result is a percentage decrease.

Change	Multiplier	New value
Increase by $r\%$	$1 + \dfrac{r}{100}$	$\text{Old} \times \left(1 + \dfrac{r}{100}\right)$
Decrease by $r\%$	$1 - \dfrac{r}{100}$	$\text{Old} \times \left(1 - \dfrac{r}{100}\right)$

Calculating percentage increase

The number of visitors to a hawker centre increased from $\displaystyle 2400$ to $\displaystyle 2760$ in one month. Find the percentage increase.

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\displaystyle \text{Increase}

\displaystyle = 2760 - 2400

\displaystyle = 360

\displaystyle \text{Percentage increase}

\displaystyle = \dfrac{360}{2400} \times 100\%

\displaystyle = 15\%

Finding the new value after a percentage decrease

A data plan originally provided $\displaystyle 10$ GB of data per month. The provider reduces this by $\displaystyle 8\%$ for a promotional tier. How much data does the new plan provide?

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\displaystyle \text{New data}

\displaystyle = (100 - 8)\% \text{ of } 10 \text{ GB}

\displaystyle = 92\% \text{ of } 10 \text{ GB}

\displaystyle = \dfrac{92}{100} \times 10

\displaystyle = 9.2 \text{ GB}

Now you try

An item costs $\$150$ . The price increased by $10\%$ . Find the new price.

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\displaystyle \text{New price}

\displaystyle = 150 \times \left(1 + \dfrac{10}{100}\right)

\displaystyle = 150 \times 1.10

\displaystyle = \$165

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