Find percentage change
The original amount is the reference. It must be positive in these questions
\[\begin{gathered}\text{Relative change}\\=\frac{\text{new}-\text{original}}{\text{original}}\end{gathered}\]
- Find the difference Use new minus original for signed change
- Divide by the original Express the difference as a share of the starting amount
- Convert the share Write the decimal ratio as an equivalent percentage \(\displaystyle -0.175=-17.5\%\)
- State the direction A signed negative change is a decrease. A question asking how much it decreased wants the size of that decrease
- Percentage points For values already expressed as percentages, subtract for the change in percentage points. Divide that difference by the starting percentage to find the relative change
Worked example
Find the signed percentage change to one decimal place
\[\begin{gathered}\text{Original mass}=96\text{ g}\\\text{New mass}=103\text{ g}\end{gathered}\]
- \(\displaystyle 103\text{ g}-96\text{ g}=7\text{ g}\)Find the increase
- \(\displaystyle \frac{7\text{ g}}{96\text{ g}}=\frac{7}{96}\)Compare the change with the original. Keep the ratio exact
- \(\displaystyle \frac{7}{96}\times100=\frac{175}{24}\)Calculate the number of percent without rounding
- \(\displaystyle \frac{175}{24}\approx7.3\)Round the percentage number to one decimal place
- \(\displaystyle \text{Percentage change}\approx7.3\%\)The positive result describes an increase
Common mistakes
Using the new amount as the base
✕\(\displaystyle \begin{gathered}\text{Relative change}\\=\frac{72-90}{72}\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Relative change}\\=\frac{72-90}{90}\end{gathered}\)
The comparison starts with the original amountComparing the new amount instead of the change
✕\(\displaystyle \begin{gathered}\text{Relative change}\\=\frac{120}{96}\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Relative change}\\=\frac{120-96}{96}\end{gathered}\)
Subtract the original before comparing the changeDropping direction
✕\(\displaystyle \begin{gathered}\text{Signed change}\\=17.5\%\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Signed change}\\=-17.5\%\end{gathered}\)
For a fall from 240 folders to 198 folders, the signed change is negative. A percentage decrease would instead be reported as a positive sizeDifficulty levels
introFind an exact whole-number percentage increase or decrease
standardFind signed changes from direct statements, tables and short contexts
challengeSelect the starting value and round a percentage with discarded digits
Questions about this topic
Which value is the denominator?+
Use the original value for the requested comparison
Why do equal dollar changes give different percentages?+
Each percentage compares the dollar change with its own original amount
Can the original value be zero?+
This calculation is undefined when the original is zero because it would require division by zero
How do percentage points differ from percentage change?+
A rate rising from 40% to 50% rises by 10 percentage points. Relative to its starting rate, the increase is 10 divided by 40, or 25%
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