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Backwards and percentage points

If you know the new value and the growth factor, you find the old one by dividing. A price after an increase is divided by a factor greater than 1. Percentage points are the difference between two percentages, with no division. From 20% to 25% is 5 percentage points. The relative increase is instead the difference divided by the first percentage. The two answers are different, and both can be right for their own question.

old=newb\text{old} = \frac{\text{new}}{b}backwards
percentage points=p2−p1\text{percentage points} = p_2 - p_1difference of percentages

Symbols

bbgrowth factor
p1, p2p_1,\ p_2the two percentages%

Example

450 NOK after a 10% increase: 4501.10≈409.09\dfrac{450}{1.10} \approx 409.09 NOK.

From 20% to 25% is 25−20=525 - 20 = 5 percentage points, but 25−2020⋅100=25\dfrac{25 - 20}{20} \cdot 100 = 25% increase.

Percentage points are a difference. Percent is a ratio.
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Part of Mathematics 1P: Percentages and growth factors.