Percentage decrease — quick, practical guide
Core idea
Percent decrease measures how much a value dropped relative to where it started.
How it works
Formula: (Original − New) ÷ Original × 100%
- New = Original × (1 − p/100)
- Original = New ÷ (1 − p/100)
Sanity checks
- Original must be > 0
- Original → 0% remaining is a 100% decrease
- Successive decreases compound (not add)
Shortcuts
- 25% decrease → ×0.75
- 40% decrease → ×0.60
Pitfalls
- Applying an increase of p% after a p% decrease doesn’t return to start
- Using the wrong base (should be the original value)
Micro‑examples
- 200 → 150: (50/200)×100 = 25% decrease
- Original from final 150 with 25% decrease: 150 ÷ 0.75 = 200
Mini‑FAQ
Can decrease exceed 100%? No—0 is the floor for the standard definition.
Action tip
Show both the decrease amount and the percent to avoid ambiguity, e.g., “−50 (−25%).”