Two discounts of 10%: why the total is 19%, not 20%
Successive percentage changes multiply. The order of the arithmetic is simple once each step is expressed as a multiplier.
Percentage change →Calculate the running price
A first 10% reduction takes 200 to 180. The second 10% reduction takes 180 to 162. The combined reduction is 38, or 38/200 = 19%. The second discount saves 18 rather than 20 because the original 200 is no longer its base. Use the discount tool for each step or enter the multiplier expression in the scientific calculator.
Use one combined multiplier
Write a reduction of p% as 1−p/100 and an increase as 1+p/100. Here 0.9 × 0.9 = 0.81, so 81% remains. Pure percentage multipliers commute: 20% off then 10% off gives the same unrounded price as the reverse order. However, a fixed coupon, a minimum spend rule or rounding after each step can make a real checkout behave differently.
Check the final comparison
Put 200 and 162 into percentage change: the output is −19%. A positive number would signal that old and new values were reversed. For an increase followed by a decrease, multiply the two corresponding factors instead of adding the rates. This approach works for chained changes with no intervening fixed additions; if an amount is added between stages, calculate that stage separately before continuing.
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