Question 1

What is a percentage?

Accepted Answer

A percentage is a fraction expressed as parts per 100 (from Latin 'per centum'). 50% = 50/100 = 0.5. To convert a decimal to percentage: multiply by 100. To convert percentage to decimal: divide by 100. Percentages are used everywhere: discounts (20% off), tax rates (VAT 10%), interest rates (APR 6.5%), test scores (90/100 = 90%), growth rates (revenue grew 15%), and probability (30% chance of rain).

Question 2

How do I calculate percentage increase or decrease?

Accepted Answer

Percentage change = ((new - old) / |old|) × 100. If a stock goes from $50 to $65: ((65-50)/50) × 100 = 30% increase. If it drops from $65 to $50: ((50-65)/65) × 100 = -23.1% decrease. Note that a 30% increase followed by a 30% decrease does NOT return to the original value — $50 × 1.30 = $65, then $65 × 0.70 = $45.50. This asymmetry is important in finance and compound growth calculations.

Question 3

What is the difference between percentage points and percentages?

Accepted Answer

Percentage points measure the arithmetic difference between two percentages; percentages measure relative change. If the interest rate rises from 2% to 3%, that is a 1 percentage point increase but a 50% relative increase ((3-2)/2 × 100 = 50%). This distinction matters in financial reporting: saying interest rates rose 50% sounds alarming; saying they rose 1 percentage point is accurate. Politicians and journalists often (accidentally or deliberately) confuse the two.

Question 4

How do I calculate what percentage X is of Y?

Accepted Answer

Formula: (X / Y) × 100. Example: 45 is what percent of 180? (45/180) × 100 = 25%. Use case: you scored 45 out of 60 on a test — (45/60) × 100 = 75%. Your team completed 120 of 200 tasks — (120/200) × 100 = 60% completion.

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