8.2Percentages Greater Than 100% and Less Than 1%

Percentages are not confined to the range $0\%$ to $100\%$ . Real life regularly produces both extremes.

Greater than 100%: The quantity exceeds the reference amount. e.g. "Café A's revenue this month is $140\%$ of last month's" means the café earned $1.4$ times last month's revenue.
Less than 1%: The quantity is an extremely small fraction of the reference. e.g. "The battery drains at $0.3\%$ per minute" means $\dfrac{0.3}{100} = 0.003$ of total capacity per minute.
$100\%$ always represents the whole, the full original amount.

Percentages outside 0%–100%

Express (i) $\displaystyle 175\%$ as a decimal and as a mixed number, and (ii) $\displaystyle 0.4\%$ as a fraction in its simplest form.

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(i)

175\% = \dfrac{175}{100}

= 1.75

= 1\dfrac{3}{4}

(ii)

0.4\% = \dfrac{0.4}{100}

= \dfrac{4}{1000}

= \dfrac{1}{250}

Now you try

Express $215\%$ as a decimal.

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\displaystyle 215\%

\displaystyle = \frac{215}{100}

\displaystyle = 2.15

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