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 \(\displaystyle \$8.1025\approx\$8.10\)
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 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)