Fraction to Decimal & Percent Converter
A Fraction to Decimal and Percent Converter changes any fraction or mixed number into an exact or rounded decimal and equivalent percentage. Divide the numerator by the denominator, then multiply by 100.
- Step 1: Express as an improper fraction: 5/8 = 5/8.
- Step 2: The fraction 5/8 is already in lowest terms.
- Step 3: Convert fraction to decimal via division: 5 ÷ 8 = 0.625 (Rounded to 4 decimals: 0.625).
- Step 4: Convert decimal to percentage by multiplying by 100: 0.625 × 100% = 62.5%.
- Note: The denominator 8 factors strictly into powers of 2 and 5, resulting in a terminating decimal.
How to Convert Fractions to Decimals & Percents
Every rational fraction represents a precise division problem: the numerator divided by the denominator. By executing long division, you transform the fraction into its decimal representation.
Because "percent" means per hundred, shifting the decimal point two places to the right (multiplying by 100) translates the decimal directly into its percentage equivalent.
Worked Example: Converting 5/8 to Decimal and Percent
A machinist is reading a blueprint with a drill bit specified as 5/8 inch. What is the measurement in decimal inches and as a percentage of an inch?
- Identify the numerator (5) and denominator (8).
- Verify if the fraction can be reduced: GCD(5, 8) = 1, so 5/8 is in lowest terms.
- Perform long division: 5 ÷ 8 = 0.625.
- Because 8 = 2³, the prime factors consist only of 2s, meaning the decimal terminates exactly without recurring digits.
- Multiply the decimal by 100 to find the percentage: 0.625 × 100% = 62.5%.
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Comprehensive Fraction to Decimal to Percent Equivalents
| Fraction | Decimal | Percentage | Decimal Type |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Terminating |
| 1/3 | 0.3333... | 33.3333% | Recurring (Period 1) |
| 1/4 | 0.25 | 25% | Terminating |
| 1/5 | 0.2 | 20% | Terminating |
| 1/6 | 0.1666... | 16.6667% | Recurring (Period 1) |
| 1/7 | 0.142857... | 14.2857% | Recurring (Period 6) |
| 1/8 | 0.125 | 12.5% | Terminating |
| 1/9 | 0.1111... | 11.1111% | Recurring (Period 1) |
| 1/10 | 0.1 | 10% | Terminating |
Common Mistakes During Fraction Conversion
To convert a decimal to a percentage, you must multiply by 100 (shifting the decimal two places to the right). A common mistake is shifting only one place (writing 0.05 as 50% instead of 5%) or shifting in the wrong direction.
Fractions like 1/3 and 2/3 have infinite decimal expansions (0.3333... and 0.6666...). Rounding to 0.33 before multiplying produces 33.0%, missing the fractional third. Always preserve full machine precision during intermediate steps.
In fraction division, the numerator is always the dividend (inside the bracket) and the denominator is the divisor (outside the bracket). Calculating 8 ÷ 5 = 1.6 instead of 5 ÷ 8 = 0.625 completely inverts the fraction.
Frequently Asked Questions
- How do you turn a fraction into a decimal?
- Divide the top number (numerator) by the bottom number (denominator). For example, 3/4 is 3 divided by 4, which equals 0.75.
- How do you convert a fraction to a percentage?
- First divide the numerator by the denominator to get the decimal, then multiply by 100 and add the percent symbol (%). For example, 1/5 = 0.20 × 100 = 20%.
- Which fractions result in terminating decimals?
- In lowest terms, a fraction produces a terminating decimal if and only if the prime factorization of its denominator contains only the prime numbers 2 and 5 (such as 2, 4, 5, 8, 10, 16, 20, 25).
- What is a repeating or recurring decimal?
- A repeating decimal is a decimal representation where one or more digits repeat infinitely at regular intervals, such as 1/3 = 0.333... or 1/7 = 0.142857142857...
- Can improper fractions be converted to percentages?
- Yes. Improper fractions (where numerator is greater than denominator) result in percentages greater than 100%. For example, 5/4 = 1.25 = 125%.