Percentage statistics one more time

So just after I finished banging my head against the wall I caught the tail-end of an item about electricity prices and we get a pretty graph. Prices increased by 9% held steady then decreased by 10%. However "the graph shows a large difference but remember it's only 1%"... gah!

Okay let's do this nice and slowly.

Imagine your bill is a nice even £100 and it increases by 9%. Now to recap that percentage means "per 100 of the total" so that's percentage number * (total/100) as our total is £100 that's £100/100 or 1 multiplied by 9 which is 9. So 9% of £100 is £9 as this is an increase it gets added to our total making £109. Everyone with me so far?

Okay so if it decreases by 10% we do exactly the same thing but with our new figures. So 10% of £109 is 10*(£109/100) or £10.90. Subtract that from our total (£109-£10.9) and we get £98.10. Still with me?

So what's the percentage difference between our starting total and our new total? In other words what percentage of our starting value of £100 would I have to remove to reach £98.10?

The difference between the two values is £1.90 so what percentage of £100 is £1.90? value/total*100 or £1.90/£100*100 which obviously neatly cancels out to 1.9%

So ignore the graph as it's only 1% difference? Nope more like 2% unless they were basing all their percentage values on the starting value which would be naughty.