Equivalent forms
A percentage is a number of hundredths. Preserve the value when changing its form
\[p\%=\frac{p}{100}\]
- Decimal to percentage Find the number of hundredths, then write the percentage \(\displaystyle 0.56=56\%\)
- 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 \(\displaystyle 6.5\%=\frac{65}{1000}=\frac{13}{200}\)
Common mistakes
Attaching a percent sign without converting
✕\(\displaystyle 0.28=0.28\%\)✓\(\displaystyle 0.28=28\%\)
The percentage number must count the decimal's hundredthsDividing in the wrong direction
✕\(\displaystyle 0.52=0.0052\%\)✓\(\displaystyle 0.52=52\%\)
Multiply by one hundred to obtain the percentage numberStopping before lowest terms
✕\(\displaystyle 26\%=\frac{26}{100}\)✓\(\displaystyle 26\%=\frac{13}{50}\)
The value is correct, but both fraction terms 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 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 a fixed number of decimal places is requested
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