Equivalent forms
A percentage is a number of hundredths. Choose the conversion direction and preserve the value
\[p\%=\frac{p}{100}\]
- Decimal to percentage Find the number of hundredths, then write the percentage \(\displaystyle \begin{aligned}0.56\times100&=56\\0.56&=56\%\end{aligned}\)
- Fraction to percentage Divide to find the decimal, then express it as a percentage \(\displaystyle \frac{7}{16}=0.4375=43.75\%\)
- Percentage to decimal Divide the percentage number by one hundred \(\displaystyle 134\%=\frac{134}{100}=1.34\)
- Percentage to fraction Write the percentage over one hundred and simplify \(\displaystyle \begin{aligned}6.5\%&=\frac{6.5}{100}\\&=\frac{65}{1000}\\&=\frac{13}{200}\end{aligned}\)
Common mistakes
Attaching a percent sign without converting
✕\(\displaystyle 0.28=0.28\%\)✓\(\displaystyle 0.28=28\%\)
The percent sign means per hundred. The percentage number must count the decimal's hundredthsDividing in the wrong direction
✕\(\displaystyle 0.52=0.0052\%\)✓\(\displaystyle 0.52=52\%\)
To express a decimal as a percentage, multiply by one hundred to obtain the percentage numberStopping before the requested lowest terms
✕\(\displaystyle 26\%=\frac{26}{100}\)✓\(\displaystyle 26\%=\frac{13}{50}\)
The first equality has the correct value, but it is unfinished when lowest terms are requested. Both parts still share a common factorDifficulty levels
introConvert one familiar value at a time in each direction
standardConvert less familiar fractions, three-place decimals and percentages above one hundred
challengeConvert small percentages and fractional percentages without unnecessary rounding
Questions about this topic
Can a percentage exceed one hundred?+
Yes. Its decimal value then exceeds one
Does converting change the value?+
No. The fraction, decimal and percentage describe the same value
Must a terminating decimal have trailing zeros?+
Only when the question requests a fixed number of decimal places. Trailing zeros do not change its value
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)