Guides/Half then double with %

Half then double with percentages

Halving is a 50% decrease; doubling is a 100% increase (or “200% of”). Doing both in sequence returns to the start — unlike equal ± percents that are not true inverses.

Factors

• −50% → ×0.5
• +100% → ×2
• 0.5 × 2 = 1 → back to the original
• Doubling language:double by percent.

Worked example

1. Start $120 → −50% → $60 → +100% → $120.
2. Contrast: +20% then −20% lands at 96% of start —± percent round trip.
3. “200% of” vs “200% increase” are different —percent of·% increase.

Percent left view

After −50%, 50% is left; doubling multiplies that remainder by 2 —percent left after a decrease.

Calculator

Percentage Calculator

Common mistakes

• Calling a double a “200% increase” (that phrasing usually means ×3, i.e. +200%).
• Halving twice and expecting −100% total — second −50% applies to the already-reduced base.