One quarter is written 1/4, 0.25, or 25%: three forms of the same value. The table gathers the equivalents people look up most, from 1/100 to 3/2, and marks which decimals terminate and which repeat without end. Here 0.75 is written with a decimal point; many other countries write 0,75 with a comma. The calculator accepts both.
| Fraction | Decimal | Percent | Type |
|---|---|---|---|
| 1/100 | 0.01 | 1% | Terminating |
| 1/20 | 0.05 | 5% | Terminating |
| 1/10 | 0.1 | 10% | Terminating |
| 1/12 | 0.083̅ | 8 1/3% ≈ 8.33% | Repeating |
| 1/8 | 0.125 | 12.5% | Terminating |
| 1/6 | 0.16̅ | 16 2/3% ≈ 16.67% | Repeating |
| 1/5 | 0.2 | 20% | Terminating |
| 1/4 | 0.25 | 25% | Terminating |
| 1/3 | 0.3̅ | 33 1/3% ≈ 33.33% | Repeating |
| 3/8 | 0.375 | 37.5% | Terminating |
| 2/5 | 0.4 | 40% | Terminating |
| 1/2 | 0.5 | 50% | Terminating |
| 3/5 | 0.6 | 60% | Terminating |
| 5/8 | 0.625 | 62.5% | Terminating |
| 2/3 | 0.6̅ | 66 2/3% ≈ 66.67% | Repeating |
| 3/4 | 0.75 | 75% | Terminating |
| 4/5 | 0.8 | 80% | Terminating |
| 7/8 | 0.875 | 87.5% | Terminating |
| 1/1 | 1 | 100% | Terminating |
| 5/4 | 1.25 | 125% | Terminating |
| 3/2 | 1.5 | 150% | Terminating |
In the repeating rows, the decimal carries a bar over the digits that repeat, and the percent is written with a fraction as the exact value; the ≈ sign marks rounding to two decimal places. For 1/12, 1/6, and 2/3 that rounding is within 1/300 of a percentage point of the exact value. All the other rows are equalities.
How to read the three columns
Fraction, decimal, and percent describe the same part of a whole. The decimal comes from dividing the numerator by the denominator. The percent is that decimal multiplied by 100, that is, how many parts out of one hundred it represents.
The repeating rows have a complete form and a rounded form. The bar over the 3 in 0.3̅ means the 3 repeats forever, like 0.333… with dots. By contrast, 0.33 stops at the second digit and equals 33/100, a little less than one third. The same care applies to the percent. The fraction form is exactly one third, and 33.33% only comes close to it.
Worked example: 7/16 as a decimal and as a percent
A row that is not in the table: what is 7/16 as a decimal and as a percent, and how do you get back to the fraction?
- Divide. 7 ÷ 16 = 0.4375.
- Multiply by 100. 0.4375 × 100 = 43.75, so 7/16 = 43.75%.
- Go back to the fraction. 43.75% = 43.75/100 = 4375/10000.
- Simplify. The greatest common factor (GCF) of 4375 and 10000 is 625, and 4375 ÷ 625 = 7 and 10000 ÷ 625 = 16.
Result: 7/16 = 0.4375 = 43.75%.
Check: 43.75% is between 37.5% (3/8) and 50% (1/2), and 7/16 lies between 3/8 and 1/2.
How to tell whether the decimal terminates
Reduce the fraction to lowest terms and look at its denominator. If it has only the factors 2 and 5, the decimal terminates. So 8 = 2 × 2 × 2 gives 0.125 and 20 = 2 × 2 × 5 gives 0.05. If any other prime appears, the decimal repeats: 12 = 2 × 2 × 3 has a 3, which is why 1/12 gives 0.083̅.
This rule works only for the reduced fraction. For example, 6/15 seems to contain a 3, but it reduces to 2/5 = 0.4. The guide to fractions with a terminating decimal proves the criterion, and the one on terminating and repeating decimals explains how the repeating ones are written.
Scaling to hundredths to read the percent
When the denominator divides 100, you do not need to divide: multiply the numerator and denominator by the same number until you reach 100. For 9/25, 25 × 4 = 100, so 9/25 = 36/100 = 36%. Scaling up does not change the value, because you multiply by 4/4, which is 1. Simplifying is the opposite step and divides top and bottom by the same number; equivalent fractions shows both directions.
If the denominator does not divide 100, divide first and multiply afterward. For 7/30, the division gives 0.2 followed by a repeating 3, and multiplied by 100 that is 70/3%, which rounds to ≈ 23.33%.
Percents greater than 100 and different totals
A percent above 100 describes an amount larger than the reference. So 5/4 = 125% is the whole plus a quarter. A negative percent appears in signed changes, such as −1/4 = −25% for a drop of one quarter.
The table works for any total, but the amount changes with it. 50% of 20 is 10 and 50% of 80 is 40, even though in both cases it is 1/2. Always write which quantity counts as 100%. To find the percent of a specific amount, use percentages.
Practice
- Write 11/20 as a decimal and as a percent.
- Write 0.45 as a fraction in lowest terms.
- Write 7/12 as a decimal and as a percent, and mark which of the two forms is exact.
See the answers
- 11/20 = 55/100 = 0.55 = 55%.
- 0.45 = 45/100 = 9/20.
- 7/12 = 0.583̅, which as a percent is 58 1/3% unrounded and ≈ 58.33% rounded.
Converting other rows
Every conversion in the table has its own tool. Fraction to decimal detects whether the result terminates or repeats, fraction to percent gives the exact value and its rounding, and percent to fraction goes the other way, giving the fraction in lowest terms. If you start from a decimal, use decimal to fraction. The other conversions, such as mixed number or improper fraction, are in conversions.
Sources
- OpenStax, Prealgebra 2e, 6.1 “Understand Percent”: defines percent as a ratio with denominator 100 (accessed October 16, 2026).
- OpenStax, Prealgebra 2e, 5.1 “Decimals”: place value of decimals (accessed October 16, 2026).