How do I calculate the percentage difference between these 2 numbers?

In a lab, I determined the percent volume of alcohol in wine: 9.65% It's an average.



If I were to compare this to what it says on the label-9.5%- how would I calculate a percent difference?How do I calculate the percentage difference between these 2 numbers?
Differences in percentage can be a little tricky to talk about,

because often percentage is used for the difference,

and it sort of wraps back on itself.



There are two ways to do this:



1) Simple subtraction

"The experiment suggests the alcohol is higher in volume by 0.15 percentage points."

It's a good idea to add the word "points" for clarity.



because ...



2) you can also do it as a ratio, just as with any quantity other than percentage (point)s.



To make it easier, let's change from percent alcohol to actual volume.

For convenience, let's say we have 1000 ml of wine.



Then the label indicates the volume of alcohol is 95 ml

but you measured 96.5 ml



96.5 / 95 = 1.015789



So there is 1.58 % more alcohol than is stated on the label.



In this case it might be even more confusing because

the two numbers start with the same digits (1 and 5) !

And both are correct in their own way.

But one is ten times the magnitude of the other.





Let's use a different example with more widely differing numbers.



Let's say in some year 25% of the households in some city had computers in the house,

and the next year it jumped to 45%.



Then you could say the increase was 20 percent or, more clearly, 20 percentage points.



But what about the ratio ?

45/25 = 1.8 ... so another way to state it is

"the number of households with computers increased by 80%".



The increase was 20 percentage points OR 80 percent (since 20 = 80% of 25).

Both are correct, but you have to make sure it is clear which you mean.