Percent change
An amount went up or down. How do you say how big the change was, in a way that means the same thing whatever size the amount started at?
Where you are 4 inside
What this area is about
Subtracting says how much something changed, but not whether that was a lot. A rise of 120 dollars is large on a rent of 400 and small on a rent of 4{,}000. Percent change measures the change against a reference amount, usually where it started, so changes to amounts of different sizes can be compared.
How these fit together
The basic measure. Percent increase and decrease divides the change by the original amount and writes the result as a percent.
The same move on a miss. Percent error measures how far an estimate sits from the true value, as a percent of the true value. The distance is an absolute value, so the error is never negative.
The multiplier. The multiplier for a percent change turns an increase of r (as a decimal) into one multiplication by 1 + r, and a decrease into one by 1 - r. Dividing by it runs a change backwards.
Changes in a row. Two percent changes one after the other multiply their multipliers. Adding the percents gives the wrong answer, because the second percent is taken of the amount after the first change.
A path through it
Start with percent increase and decrease. Percent error can come next or at any later point. The multiplier comes after percent increase, and successive changes after the multiplier.
Finish here and discounts and sales tax, markup and margin, simple interest and growth and decay factors all build on it.