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Common Percentage Formulas
| Goal | Formula |
|---|---|
| X% of Y | (X ÷ 100) × Y |
| X is what % of Y | (X ÷ Y) × 100 |
| Discount price | Original − (Original × Discount%/100) |
| % Change | ((New − Old) ÷ |Old|) × 100 |
| % Increase | ((New − Old) ÷ Old) × 100 (positive) |
| % Decrease | ((Old − New) ÷ Old) × 100 (positive) |
Percentage Calculator FAQ
Common questions about calculating percentages.
Multiply the number by the percentage, then divide by 100. Example: 20% of 150 = 150 × 20 ÷ 100 = 30. Use the "What is X% of Y?" option above.
Use the formula: ((New Value − Old Value) ÷ |Old Value|) × 100. A positive result is a percentage increase; negative is a decrease. Select "Percentage Change" from the dropdown above.
Enter the original price and discount percentage in the "Discount Calculator" mode. The result shows the discount amount and final price. Formula: Final = Original × (1 − Discount%/100).
Most basic calculators display 8–10 significant figures. Scientific calculators (like the TI-30 or Casio fx-300) typically show 10–12 sig figs internally. When rounding for significant figures in homework or lab work, your answer should match the fewest sig figs among your inputs. Example: 2.5 × 3.42 = 8.6 (rounded to 2 sig figs, the precision of 2.5).
Calculators convert your keystrokes into binary numbers (0s and 1s), process them through logic gate circuits on a microchip, then convert the result back to decimal for display. They follow operator precedence rules (multiplication before addition) using an internal parsing algorithm. Scientific calculators also store constants, support trigonometric functions, and maintain extra internal precision to minimize rounding errors.
Use the digit-by-digit method or Newton's method. For Newton's method: pick a guess g, then iterate: g_new = (g + n/g) / 2 until it converges. Example: √50 — guess g=7, next: (7 + 50/7)/2 = (7 + 7.14)/2 ≈ 7.07. One more pass: (7.07 + 50/7.07)/2 ≈ 7.071. That's correct to 3 decimal places after just 2 steps. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) are worth memorizing.