The Nines Complement

Adding 9 to any number has a neat shortcut: add 10 and subtract 1. So 56 + 9 = 66 - 1 = 65. This extends to 99 (add 100, subtract 1) and 999 (add 1000, subtract 1). The pattern works because 9 is always one less than a power of ten.

Cashiers used a related idea for centuries when making change. If something costs $3.47 and you pay $5, they count up: $3.47 + $0.03 = $3.50, + $0.50 = $4.00, + $1.00 = $5.00, so the change is $1.53. This counting-up method avoids subtraction entirely and keeps errors low.