Visual Fraction to Decimal, Percent & Ratio Converter
Every rational number $\frac{a}{b}$ maps to a decimal via $d = a \div b$ and to a percentage via $P\% = 100 \times \frac{a}{b}$; the decimal terminates if and only if the reduced denominator's prime factors belong exclusively to $\{2, 5\}$.
a/b = (a ÷ b)_10 = (100 × a / b)%Inputs & Parameters (4)
20-Row Comparison Table
| # | Primary Numerator (a) | Combined Sum (A + B) | Reduced Sum | Sum % |
|---|---|---|---|---|
| 01 | 0 | 0.6 | 3/5 | 60% |
| 02 | 1 | 0.725 | 29/40 | 72.5% |
| 03 | 2 | 0.85 | 17/20 | 85% |
| 04 | 3 | 0.975 | 39/40 | 97.5% |
| 05 | 4 | 1.1 | 11/10 | 110% |
| 06 | 5 (Current) | 1.225 | 49/40 | 122.5% |
| 07 | 6 | 1.35 | 27/20 | 135% |
| 08 | 7 | 1.475 | 59/40 | 147.5% |
| 09 | 8 | 1.6 | 8/5 | 160% |
| 10 | 9 | 1.725 | 69/40 | 172.5% |
| 11 | 11 | 1.975 | 79/40 | 197.5% |
| 12 | 12 | 2.1 | 21/10 | 210% |
| 13 | 13 | 2.225 | 89/40 | 222.5% |
| 14 | 14 | 2.35 | 47/20 | 235% |
| 15 | 15 | 2.475 | 99/40 | 247.5% |
| 16 | 16 | 2.6 | 13/5 | 260% |
| 17 | 17 | 2.725 | 109/40 | 272.5% |
| 18 | 18 | 2.85 | 57/20 | 285% |
| 19 | 19 | 2.975 | 119/40 | 297.5% |
| 20 | 20 | 3.1 | 31/10 | 310% |
Key Analytical Takeaways
- 01Denominators that divide powers of 10 ($2, 4, 5, 8, 10, 16, 20$) produce clean terminating decimals (e.g., $5/8 = 0.625 = 62.5\%$).
- 02Denominators containing prime factors like $3, 7, 11,$ or $13$ produce repeating periodic decimals (e.g., $2/3 = 0.\overline{6} = 66.\overline{6}\%$).
- 03Comparing two fractions on the normalized $100\%$ scale reveals exact percentage-point differences at a glance.
Frequently Asked Questions
How can you tell if a fraction will become a terminating or repeating decimal?+
First reduce the fraction by its GCD. If the simplified denominator has only 2 and/or 5 as prime factors, the decimal terminates; any other prime factor (3, 7, 11, etc.) causes a repeating decimal.
How do you convert a fraction into a percentage?+
Divide the numerator by the denominator and multiply the decimal result by 100 (moving the decimal point two places right).
How can you tell if a simplified fraction terminates or repeats in decimal?+
A fully reduced fraction a/b terminates in base 10 if and only if the prime factorization of denominator b contains exclusively 2s and 5s (the prime factors of 10); any other prime factor produces a repeating decimal.