Percent vs percentage points (news and finance)
If an interest rate rises from 3% to 5%, that is an increase of 2 percentage points. It is also a relative increase of about 66.7% from the old rate (because (5−3)/3 ≈ 0.667). Headlines often say “rates up 2%” when they mean 2 percentage points — always ask which base they use.
Percentage change: old value must be the denominator
“Percent change” = (new − old) ÷ old. Swapping new and old in the denominator flips the sign and magnitude. Use the Percentage Change Calculator when the numbers are not intuitive, and double-check which column is “before” vs “after.”
Stacked discounts are multiplicative, not additive
“30% off, then an extra 20% off” applies 20% to the reduced price, not to the original. You do not get 50% off the tag. Multiply the remaining fractions: 0.7 × 0.8 = 0.56 → 44% off the original. The Discount Calculator is built for this structure.
Mental math that usually works
10% of a number moves the decimal one place left. Five percent is half of ten percent. Twenty percent is double ten percent. Use these as sanity checks against typed inputs — especially for tips and sale prices.
How to verify before you pay
For a single-step discount, compare price × (1 − rate) to the register. For successive discounts, apply each step to the running price or use one combined multiplier as above. If tax is involved, know whether tax applies to the discounted subtotal in your jurisdiction (rules vary).