Percent change shows how much a value grew or shrank; percent error shows how accurate a measurement is!
PERCENT CHANGE measures how much a quantity increased or decreased, expressed as a percentage of the original. If the new value is greater, it is a percent increase; if less, a percent decrease. PERCENT ERROR compares a measured value to the known true value.
A shirt originally costs $40. It now costs $50. Percent change = (50 − 40) / 40 × 100% = 10 / 40 × 100% = 0.25 × 100% = 25% increase!
A phone was $600. Now it is $480. Percent change = (480 − 600) / 600 × 100% = −120 / 600 × 100% = −0.20 × 100% = −20% (a 20% decrease)
You measure a rod as 49.5 cm. The true length is 50 cm. Percent error = |49.5 − 50| / 50 × 100% = 0.5 / 50 × 100% = 1% error
A tree was 80 cm tall last year. This year it is 100 cm. What is the percent increase?
Remember This!
Always divide by the ORIGINAL value (not the new one) when calculating percent change. Using the new value gives a different — and wrong — percentage.