Percentage Change and Reverse Percentage

We use percentage change to show the difference of a quantity relative to its original value.

In general,

for percentage increase, \({ x\% = \frac{\mathrm{Increment}}{\mathrm{Original \ value}} \times 100\% }\)

for percentage decrease, \({x\% = \frac{\mathrm{Decrement}}{\mathrm{Original \ value}} \times 100\%}\)

Reversing a percentage change requires a nonzero multiplier. A \(100\%\) decrease gives zero regardless of the original value, so the original cannot be recovered from that result alone.