Percentages fail most often in one place: successive changes do not cancel. A price that rises 10% and then falls 10% does not return to its start, because the fall acts on the higher price.
Worked example: start at 100. Rise 10% gives 110. Fall 10% of 110 gives 110 - 11 = 99. Net change: 1% decrease. The formula for two successive changes of a% and b% is a + b + (a times b)/100, with signs: 10 - 10 + (10 times -10)/100 = -1. One formula replaces a page of confusion.