Percentage of a quantity
Identify the quantity that the percentage applies to. Convert the percentage, multiply, then round if required
\[p\%\text{ of }Q=\frac{p}{100}Q\]
- Convert the percentage Use a fraction or an exact decimal \(\displaystyle 17.5\%=\frac{7}{40}=0.175\)
- Keep the base and unit A percentage of a money amount is another money amount \(\displaystyle 0.175\times\$46.30=\$8.1025\)
- Apply the final precision For money, use cents when the question requires it \(\displaystyle \$8.1025\approx\$8.10\)
Worked example
Find the amount reserved for materials, to the nearest cent
\[\begin{gathered}\text{Budget}=\$94.60\\\text{Materials share}=18.5\%\end{gathered}\]
- \(\displaystyle 18.5\%=0.185\)Convert the percentage into its decimal multiplier
- \(\displaystyle \begin{gathered}\text{Materials amount}\\=0.185\times\$94.60\end{gathered}\)Apply that multiplier to the whole budget
- \(\displaystyle =\$17.501\)Keep the product exact before rounding
- \(\displaystyle \approx\$17.50\)Round the final amount to the nearest cent
Common mistakes
Using the percentage number directly
✕\(\displaystyle 22\%=22\)✓\(\displaystyle 22\%=0.22\)
The percentage number counts hundredths. Convert it before using it as a multiplierDividing to find a share
✕\(\displaystyle 22\%\text{ of }\$68=\$68\div0.22\)✓\(\displaystyle 22\%\text{ of }\$68=0.22\times\$68\)
Finding a percentage of a known quantity uses multiplicationRounding the multiplier
✕\(\displaystyle 18.5\%=0.2\)✓\(\displaystyle 18.5\%=0.185\)
Rounding the percentage first changes the requested shareDifficulty levels
introFind familiar percentages with exact answers
standardApply general whole-number percentages to money and measurements
challengeApply fractional percentages and round money or measurements when needed
Questions about this topic
Can the percentage amount exceed the starting quantity?+
Yes, if the percentage exceeds one hundred
Why keep the original unit?+
The calculation scales the quantity. It does not change what the quantity measures
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 1: Percentages and ratios
In this chapter
Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1A Percentages: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changeAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceExpress a ratio in simplest formComplete an equivalent ratioDivide a quantity in a given ratio1E Dividing in a ratio: Use one known part of a ratio to find the others1F Unitary method: Find the original amount from a percentage1F Unitary method: Use one known part of a ratio to find the othersScale a proportional quantity with the unitary methodDecide which option is the better value