A change in percentage points is the plain gap between two rates. A percentage change divides that gap by the starting rate. They describe the same movement but give different numbers.
This lesson is part of rates and percentages in multistep consumer questions. All rates are invented.
How do I work out both?
Use the same two steps each time.
- Percentage points = new rate − old rate.
- Percentage change = (new rate − old rate) ÷ old rate × 100.
Worked example: an original table
| Situation | Old rate | New rate | Change in points | Percentage change |
|---|---|---|---|---|
| Customers paying by e-wallet at a stall | 30% | 36% | +6 points | 6 ÷ 30 × 100 = +20% |
| A saving rate at a fictional bank | 2.0% | 2.5% | +0.5 points | 0.5 ÷ 2 × 100 = +25% |
| A loan rate | 6% | 9% | +3 points | 3 ÷ 6 × 100 = +50% |
| A discount rate | 5% | 4% | −1 point | −1 ÷ 5 × 100 = −20% |
Each row shows the same movement two ways: the plain gap, and the gap compared with the old rate. The wording of the question tells you which one to write.
The mistake that mixes the two
A common slip is to say the e-wallet share “rose by 6%”. That sentence is unclear, because 6% of what?
Say “6 percentage points” for the gap, or “rose by 20%” for the percentage change. When you give a percentage change, say what it is a percentage of.
Check yourself
A rate falls from 8% to 6%. State the change in percentage points and the percentage change.
Answer
Percentage points: 6 − 8 = −2 points.
Percentage change: −2 ÷ 8 × 100 = −25%.
The fall is 2 points but 25% of the starting rate.
What to study next
Apply percentage bases to plans with fees in comparing instalment totals using supplied fees. Explore bases in the percentage base and index explorer.
If you want a teacher to check your wording of changes, see online one-to-one Mathematics tuition.