% Percent to Decimal Converter
Professional Percentage ⇄ Decimal Converter | Quick % to Decimal Calculator
📊 Common Percent-Decimal Conversions
| Percent | Decimal | Fraction | Percent | Decimal | Fraction |
|---|---|---|---|---|---|
| 1% | 0.01 | 1/100 | 50% | 0.5 | 1/2 |
| 5% | 0.05 | 1/20 | 60% | 0.6 | 3/5 |
| 10% | 0.1 | 1/10 | 75% | 0.75 | 3/4 |
| 12.5% | 0.125 | 1/8 | 80% | 0.8 | 4/5 |
| 20% | 0.2 | 1/5 | 90% | 0.9 | 9/10 |
| 25% | 0.25 | 1/4 | 100% | 1.0 | 1/1 |
| 33.33% | 0.3333 | 1/3 | 125% | 1.25 | 5/4 |
| 40% | 0.4 | 2/5 | 150% | 1.5 | 3/2 |
📚 Complete Guide to Percent-Decimal Conversion
Understanding Percentages and Decimals
Percent means "per hundred" from Latin "per centum". Symbol % represents division by 100. Historical origin: Roman tax calculations used centesimal (hundredth) divisions. Modern usage: Percentages express proportions, rates, changes, statistics in standardized format. Formula foundation: \( \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \). Example: 3 out of 4 = \( \frac{3}{4} \times 100 = 75\% \). Decimal system represents fractions with denominators of powers of 10. Decimal point separates whole numbers from fractional parts. Position right of decimal: tenths \( (10^{-1}=0.1) \), hundredths \( (10^{-2}=0.01) \), thousandths \( (10^{-3}=0.001) \). Example: 0.75 = \( 7 \times 0.1 + 5 \times 0.01 = \frac{75}{100} = \frac{3}{4} \). Universal in science, engineering, finance for precise fractional representation. Relationship between percent and decimal: Both represent same fractional value in different formats. Percent emphasizes "out of 100" (75% = 75 out of 100). Decimal shows direct fractional value (0.75 = three-quarters). Conversion factor: 100 (percent to decimal: divide; decimal to percent: multiply). Mathematical equivalence: 50% = 0.50 = 0.5 = \( \frac{50}{100} = \frac{1}{2} \). Why two formats exist: Percentages intuitive for comparisons (75% vs 80% easier than 0.75 vs 0.80). Decimals better for calculations (0.75 × 200 simpler than 75% × 200). Context determines preference: discounts use % (25% off), probabilities use decimals (0.25 chance), interest rates use % (5% APR). Historical development: Ancient civilizations used fractions (Egypt: 1/2, 1/4; Babylon: base-60). Roman centesimal system: hundredths for taxes, measurements. Percent symbol % evolved from "per 100" → "p 100" → "%" (15th century Italy). Decimal point introduced by Simon Stevin (1585), popularized by John Napier (1617). Modern standard: Decimals for computation, percents for communication.
Percent to Decimal Conversion Formula
Core formula: Decimal = Percent ÷ 100. Mathematical justification: Percent symbol % means "÷100". Example: 75% literally means 75÷100. Remove % sign and divide by 100 to get decimal. Step-by-step procedure: (1) Remove percent sign (%). (2) Divide the number by 100. (3) Result is decimal equivalent. Alternative method: Move decimal point 2 places left. Why this works: Dividing by 100 = moving decimal 2 places left (100 = 10²). Quick mental math technique. Example: 75% → 75.0 → 0.75 (moved 2 left). Detailed Example 1: Convert 75% to decimal. Method 1 (Division): 75% = 75 ÷ 100 = 0.75. Calculation: \( \frac{75}{100} = 0.75 \). Method 2 (Decimal shift): 75% → 75.0 → 0.75 (shift left 2). Result: 75% = 0.75. Meaning: 75 out of 100 = three-quarters = 0.75. Detailed Example 2: Convert 50% to decimal. 50% = 50 ÷ 100 = 0.50 = 0.5. Fraction: \( \frac{50}{100} = \frac{1}{2} = 0.5 \). Meaning: Half, one-half, 0.5. Detailed Example 3: Convert 8% to decimal. 8% = 8 ÷ 100 = 0.08. Decimal shift: 8% → 8.0 → 0.08 (two places left, add leading zero). Fraction: \( \frac{8}{100} = \frac{2}{25} = 0.08 \). Detailed Example 4: Convert 125% to decimal. 125% = 125 ÷ 100 = 1.25. Greater than 1 (more than 100%). Meaning: 125 out of 100 = one and a quarter. Example: 125% of 200 = 1.25 × 200 = 250. Detailed Example 5: Convert 0.5% to decimal. 0.5% = 0.5 ÷ 100 = 0.005. Small percentage requires three decimal places. Decimal shift: 0.5 → 0.005 (move left 2 places). Meaning: Half of one percent, 5 per thousand. Detailed Example 6: Convert 12.5% to decimal. 12.5% = 12.5 ÷ 100 = 0.125. Fraction: \( \frac{12.5}{100} = \frac{125}{1000} = \frac{1}{8} = 0.125 \). Meaning: One-eighth, 12.5 hundredths. Common pattern recognition: 100% = 1.0 (whole). 50% = 0.5 (half). 25% = 0.25 (quarter). 10% = 0.1 (tenth). 1% = 0.01 (hundredth). 0.1% = 0.001 (thousandth).
Decimal to Percent Conversion Formula
Core formula: Percent = Decimal × 100. Inverse of percent-to-decimal conversion. Multiply decimal by 100 and add % symbol. Alternative method: Move decimal point 2 places right, add %. Why: Multiplying by 100 moves decimal right 2 places. Quick mental calculation. Example: 0.75 → 75.0 → 75% (shift right 2). Step-by-step procedure: (1) Take decimal value. (2) Multiply by 100. (3) Add percent sign (%). Detailed Example 1: Convert 0.75 to percent. Method 1 (Multiplication): 0.75 × 100 = 75%. Calculation: \( 0.75 \times 100 = 75 \). Method 2 (Decimal shift): 0.75 → 75. → 75% (shift right 2). Result: 0.75 = 75%. Detailed Example 2: Convert 0.5 to percent. 0.5 × 100 = 50%. Equivalence: 0.5 = 0.50 = 50%. Fraction: \( \frac{1}{2} = 0.5 = 50\% \). Detailed Example 3: Convert 0.08 to percent. 0.08 × 100 = 8%. Decimal shift: 0.08 → 08. → 8%. Small decimal becomes single-digit percent. Detailed Example 4: Convert 1.25 to percent. 1.25 × 100 = 125%. Greater than 1 = over 100%. Meaning: One and a quarter = 125%. Example: Test score 1.25× average = 125% of average. Detailed Example 5: Convert 0.005 to percent. 0.005 × 100 = 0.5%. Very small decimal = fraction of percent. Decimal shift: 0.005 → 00.5 → 0.5%. Alternative: 5 per thousand = 0.5%. Detailed Example 6: Convert 0.125 to percent. 0.125 × 100 = 12.5%. Decimal shift: 0.125 → 12.5 → 12.5%. Fraction: \( \frac{1}{8} = 0.125 = 12.5\% \). Detailed Example 7: Convert 2.0 to percent. 2.0 × 100 = 200%. Double = twice = 200%. Meaning: Two times, 200 out of 100. Example: Population doubled = increased to 200% of original.
Practical Applications and Examples
Discounts and Sales: Store advertises 25% off. Convert to decimal for calculation: 25% = 0.25. Original price $80. Discount = 0.25 × $80 = $20 off. Sale price = $80 - $20 = $60. Alternative: Pay 75% of original (100% - 25% = 75% = 0.75). Sale price = 0.75 × $80 = $60 directly. Tax Calculations: Sales tax 8.5% on $50 purchase. Convert: 8.5% = 0.085. Tax amount = 0.085 × $50 = $4.25. Total = $50 + $4.25 = $54.25. Alternative formula: Total = Price × (1 + tax rate) = $50 × 1.085 = $54.25. Interest Rates: Credit card APR 18.99%. Convert to decimal: 18.99% = 0.1899. Monthly rate = 0.1899 ÷ 12 = 0.0158 (1.58% monthly). Interest on $1000 balance = $1000 × 0.0158 = $15.80 monthly. Compound interest formula uses decimal: \( A = P(1 + r)^n \) where r = 0.1899. Probabilities and Statistics: Weather forecast: 70% chance rain. Decimal probability: 0.70 or 0.7. Calculation: If 70% rain chance, 30% no rain (1 - 0.7 = 0.3 = 30%). Combined probability (rain both days): 0.7 × 0.7 = 0.49 = 49%. Grade Calculations: Student scored 85% on test. Convert: 85% = 0.85. Test worth 20% of final grade: 0.85 × 0.20 = 0.17 = 17% contribution to final. If four tests: (0.85 + 0.90 + 0.78 + 0.92) ÷ 4 = 0.8625 = 86.25% average. Business Metrics: Profit margin 12.5% means profit = 12.5% of revenue. Convert: 12.5% = 0.125. Revenue $500k → Profit = 0.125 × $500k = $62.5k. Growth rate 15% annually = multiply by 1.15 each year (1 + 0.15). After 5 years: \( \text{Value} \times 1.15^5 = \text{Value} \times 2.011 \) (doubled). Nutritional Information: Food label: 20% daily value sodium per serving. Convert: 20% = 0.20. If daily limit 2300mg: This serving = 0.20 × 2300mg = 460mg sodium. Five servings = 5 × 0.20 = 1.00 = 100% (full daily amount). Concentration and Mixtures: Solution is 5% acid by volume. Convert: 5% = 0.05. In 200mL solution: Acid volume = 0.05 × 200mL = 10mL. Water volume = 200mL - 10mL = 190mL. Dilute to 2%: Need 0.02 = 10mL ÷ total, so total = 500mL (add 300mL water).
Common Percent-Decimal Conversions Table
| Percent | Decimal | Fraction | Common Use |
|---|---|---|---|
| 1% | 0.01 | 1/100 | Small discount, tax adjustment |
| 5% | 0.05 | 1/20 | Sales tax (some states), tips |
| 10% | 0.1 | 1/10 | Quick tip calculation, decimal place |
| 12.5% | 0.125 | 1/8 | One-eighth, fractional percent |
| 15% | 0.15 | 3/20 | Standard tip, service charge |
| 20% | 0.2 | 1/5 | Good tip, common discount |
| 25% | 0.25 | 1/4 | Quarter, major discount |
| 33.33% | 0.3333 | 1/3 | One-third, split 3 ways |
| 40% | 0.4 | 2/5 | Large discount |
| 50% | 0.5 | 1/2 | Half, 50-50 split |
| 60% | 0.6 | 3/5 | Majority, passing grade |
| 66.67% | 0.6667 | 2/3 | Two-thirds, supermajority |
| 75% | 0.75 | 3/4 | Three-quarters, good grade |
| 80% | 0.8 | 4/5 | Strong majority, B grade |
| 90% | 0.9 | 9/10 | A grade, high probability |
| 100% | 1.0 | 1/1 | Whole, complete, full |
| 125% | 1.25 | 5/4 | 125% effort, over target |
| 150% | 1.5 | 3/2 | 1.5× increase, 50% growth |
| 200% | 2.0 | 2/1 | Double, twice, 100% increase |
Why Choose RevisionTown's Percent-Decimal Converter?
RevisionTown's professional converter provides: (1) Bidirectional Conversion—Convert percent→decimal and decimal→percent seamlessly with instant results; (2) Step-by-Step Calculation—Shows complete division/multiplication process with formula explanation for educational understanding; (3) Flexible Input—Accepts percentages with or without % symbol, handles decimals, integers, fractions; (4) Unlimited Precision—Handles very small (0.001%) and very large (10000%) percentages accurately; (5) Copy to Clipboard—One-click copy for immediate use in calculations, spreadsheets, documents; (6) Comprehensive Reference Table—Quick lookup for common conversions (1%, 5%, 10%, 25%, 50%, 75%, 100%); (7) Fraction Equivalents—Shows fraction representation alongside percent and decimal (25% = 0.25 = 1/4); (8) Mobile Optimized—Responsive design works perfectly on smartphones, tablets, desktops; (9) Zero Cost—Completely free with no ads, registration, or limitations; (10) Professional Accuracy—Trusted by students, teachers, financial professionals, engineers, scientists, business analysts, and shoppers worldwide for academic studies (converting test scores, grade percentages to GPA decimals), financial calculations (interest rates, tax rates, discount calculations, investment returns), retail shopping (calculating sale prices, comparing discounts in decimal form), business analytics (profit margins, growth rates, market share conversions), scientific research (concentration percentages, probability calculations, statistical analysis), cooking and recipes (scaling percentages to decimal multipliers), construction and engineering (material percentages, tolerance specifications), healthcare (medication dosages, solution concentrations), sports statistics (shooting percentages, win rates in decimal form), data analysis (converting survey percentages for mathematical operations), and all applications requiring accurate percent-decimal conversions with professional-grade tools for education, finance, business, science, and everyday calculations worldwide.
❓ Frequently Asked Questions
Divide by 100 or move decimal point 2 places left. Formula: Decimal = Percent ÷ 100. Symbol % means "per hundred" = divide by 100. Method 1 (Division): Remove % sign, divide by 100. 75% = 75 ÷ 100 = 0.75. Calculation: \( \frac{75}{100} = 0.75 \). Method 2 (Decimal shift): Move decimal point 2 places left. 75% → 75.0 → 0.75 (shift left twice). Faster for mental math. Examples: 50% = 50 ÷ 100 = 0.5 (half). 8% = 8 ÷ 100 = 0.08 (add leading zero). 125% = 125 ÷ 100 = 1.25 (over 1.0). 0.5% = 0.5 ÷ 100 = 0.005 (very small). 12.5% = 12.5 ÷ 100 = 0.125 (one-eighth). Why this works: Percent = "per 100". 75% = 75 per 100 = 75/100 = 0.75. Dividing by 100 converts to decimal form. Quick check: Result should be 100× smaller. 75% → 0.75 (75 became 0.75). 100% = 1.0 (baseline). Values under 100% give decimals under 1.0.
Multiply by 100 and add % sign. Formula: Percent = Decimal × 100. Inverse of percent-to-decimal conversion. Method 1 (Multiplication): Multiply decimal by 100, add %. 0.75 × 100 = 75%. Calculation: \( 0.75 \times 100 = 75 \). Method 2 (Decimal shift): Move decimal point 2 places right, add %. 0.75 → 75. → 75% (shift right twice). Quick mental method. Examples: 0.5 = 0.5 × 100 = 50% (half). 0.08 = 0.08 × 100 = 8%. 1.25 = 1.25 × 100 = 125% (over 100%). 0.005 = 0.005 × 100 = 0.5%. 0.125 = 0.125 × 100 = 12.5%. 2.0 = 2.0 × 100 = 200% (double). Why this works: Decimal is fraction with denominator power of 10. Multiplying by 100 converts to "per hundred" format. 0.75 = 75/100 = 75%. Quick check: Result should be 100× larger. 0.75 → 75% (0.75 became 75). Decimals under 1.0 give percents under 100%. Decimals over 1.0 give percents over 100%.
75% = 0.75 (decimal). Conversion: 75% = 75 ÷ 100 = 0.75. Decimal shift: 75.0 → 0.75 (move left 2 places). Fraction: \( \frac{75}{100} = \frac{3}{4} = 0.75 \). Meaning: Three-quarters, 75 out of 100, 0.75 of whole. Common uses: (1) Grades: 75% score = 0.75 × total points. (2) Discounts: Item priced at 75% = multiply by 0.75. Example: $100 item at 75% price = $100 × 0.75 = $75. (3) Probability: 75% chance = 0.75 probability. Related conversions: 75% = 0.75 = 3/4 (all equivalent). 25% = 0.25 = 1/4 (complement to 100%). 50% = 0.5 = 1/2 (half). 100% = 1.0 = whole. Calculation example: Find 75% of 200. Method: 0.75 × 200 = 150. Verification: 75% of 200 = (75/100) × 200 = 150 ✓.
0.5 = 50% (percent). Conversion: 0.5 × 100 = 50%. Decimal shift: 0.5 → 50. → 50% (move right 2 places). Fraction: \( 0.5 = \frac{1}{2} = \frac{50}{100} = 50\% \). Meaning: Half, one-half, 50 out of 100. Common contexts: (1) Probability: Coin flip = 0.5 probability heads = 50% chance. (2) Discounts: Half off = 50% discount. (3) Grades: Half credit = 50% of points. (4) Growth: 50% increase = multiply by 1.5 (1 + 0.5). Equivalences: 0.5 = 0.50 = 50% = 1/2 (all same value). Decimal 0.5 often written 0.50 for clarity with percents. Related values: 0.25 = 25% (quarter). 0.75 = 75% (three-quarters). 1.0 = 100% (whole). 1.5 = 150% (1.5 times). Calculation example: 50% of 80. Method: 0.5 × 80 = 40. Quick: Half of 80 = 40.
0.08 = 8% (percent). Conversion: 0.08 × 100 = 8%. Decimal shift: 0.08 → 08. → 8% (move right 2 places). Fraction: \( 0.08 = \frac{8}{100} = \frac{2}{25} = 8\% \). Step-by-step: Start with 0.08. Multiply by 100: 0.08 × 100 = 8. Add percent sign: 8%. Common uses: (1) Sales tax: 8% tax rate in many states. (2) Interest: Credit card cash advance fee 8%. (3) Concentration: 8% alcohol by volume in strong beer. Related conversions: 0.08 = 8% = 8/100 = 2/25 (simplified fraction). 0.8 = 80% (ten times larger). 0.008 = 0.8% (ten times smaller). 8 = 800% (100 times larger). Why leading zero matters: 0.08 ≠ 0.8. 0.08 = 8% (small). 0.8 = 80% (large). Leading zero crucial for correct value. Calculation example: 8% of $500. Convert: 8% = 0.08. Calculate: 0.08 × $500 = $40.
Percent = "per hundred" from Latin "per centum". Symbol % represents division by 100. Mathematical definition: Percent expresses ratio as fraction with denominator 100. Formula: \( \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \). Etymology: Latin "per centum" = "by the hundred". Italian "per cento" shortened to %. Symbol evolved: "per 100" → "p 100" → "%" (15th-16th century). Examples: 50% = 50 per 100 = 50/100 = half. 75% = 75 per 100 = 75/100 = three-quarters. 100% = 100 per 100 = whole. 125% = 125 per 100 = more than whole. Why use percents: (1) Standardization: Compare values on common scale (0-100). (2) Intuitive: "Out of 100" easy to visualize. (3) Communication: 75% clearer than 0.75 for general audience. (4) Historical: Roman tax system used hundredths. Common contexts: Discounts (25% off). Grades (85% score). Interest (5% APR). Probability (60% chance). Growth (10% increase). Statistics (45% approval). Concentration (2% milk fat). Mathematical operations: Add/subtract: Must convert to decimal first. 50% + 25% = 0.5 + 0.25 = 0.75 = 75%. Multiply: 50% of 80% = 0.5 × 0.8 = 0.4 = 40%.
Multiply decimal by 100, add % sign. Works for any decimal value. Formula: Percent = Decimal × 100. Alternative: Shift decimal point 2 places right. Step-by-step examples: Example 1: 0.75 to percent. 0.75 × 100 = 75. Add %: 75%. Example 2: 0.125 to percent. 0.125 × 100 = 12.5. Result: 12.5%. Example 3: 1.5 to percent. 1.5 × 100 = 150. Result: 150% (over 100%). Example 4: 0.005 to percent. 0.005 × 100 = 0.5. Result: 0.5% (fractional percent). Example 5: 0.3333 to percent. 0.3333 × 100 = 33.33. Result: 33.33% (repeating, ≈1/3). Special cases: 1.0 = 100% (whole, baseline). 0.0 = 0% (nothing). 2.0 = 200% (double). 0.01 = 1% (one hundredth). Verification: Convert back: 75% ÷ 100 = 0.75 ✓. Round-trip should equal original decimal. Practical use: Calculator shows 0.15, want percent: 0.15 × 100 = 15%. Tip calculator: Decimal 0.18 = 18% tip.
100% = 1.0 (decimal). Represents whole, complete, full amount. Conversion: 100% = 100 ÷ 100 = 1.0. Fraction: \( \frac{100}{100} = 1 \). Decimal: 1.0 or simply 1 (trailing zero optional). Meaning: Entire amount, whole, complete, all of it. Baseline for comparisons. Examples: 100% effort = full effort. 100% juice = pure juice. 100% cotton = all cotton. Why important: Reference point for other percentages. Below 100% = partial amount. Above 100% = more than original. Calculations: Multiplying by 1.0 leaves number unchanged (identity). Related values: 50% = 0.5 (half of 100%). 75% = 0.75 (three-quarters of 100%). 125% = 1.25 (quarter more than 100%). 200% = 2.0 (twice 100%). Percent change formula: Original = 100% baseline. Increase to 125% = 25% increase (125% - 100% = 25%). Decrease to 75% = 25% decrease (100% - 75% = 25%). Practical examples: Battery at 100% = 1.0 × capacity = full charge. Test score 100% = 1.0 × total points = perfect score. 100% price = 1.0 × list price = full price (no discount).
