Percentage difference between numbers

[pojzon]

Hi!
I'm trying to understand something, I'm not very good at math.
I got something like that:


I'm comparing two numbers to see what was the increase/decrease.
After adding 16% to next example, I would think that percentage difference between them would also be 16%, but that is not the case.
How should I understand it?
Thank you!

 

[Dr.Peterson]

Hi!
I'm trying to understand something, I'm not very good at math.
I got something like that:
View attachment 37718

I'm comparing two numbers to see what was the increase/decrease.
After adding 16% to next example, I would think that percentage difference between them would also be 16%, but that is not the case.
How should I understand it?
Thank you!

As I understand it, you found that 152 is a 69% increase from 90; then you increased the 152 by 16% to get 176.32, which is a 96% increase from 90.

Why do you expect the percent to have increased by 16%? I avoid expecting different percentages to add up, when they have different bases.

Here's what's really happening:

[math]\frac{152 - 90}{90}\approx0.69\\\frac{152\cdot1.16 - 90}{90}\approx0.96[/math]
So the change in the percent change is [math]\frac{152\cdot1.16-90}{90}-\frac{152-90}{90}=\frac{(152\cdot1.16-90)-(152-90)}{90}=\frac{152\cdot1.16-152}{90}=\frac{152\cdot0.16}{90}\approx1.69\cdot0.16\approx0.27[/math]
So the 16% has itself been increased by 69%