FRACTION
Fractions, decimals, percentages, one family.
The three notations are the same number. Pick how you want to type it and get the other two, automatically reduced to lowest terms, with repeating decimals flagged (1/3 = 0.333…).
Everything runs locally in your browser
How to use
Choose how to type the number: fraction (numerator and denominator, denominator not 0), decimal or percentage. The result panel gives all three notations, with repeating decimals flagged together with their repeating block and an approximation. The quick-reference table below lists the eight most-tested fractions.
Common questions
How do percentages and decimals differ?
A percentage means "per hundred": 50% = 50/100 = 0.5. Remove the % sign and shift the decimal point two places left to get the decimal.
What is a repeating decimal?
A decimal that does not terminate repeats a block: 1/3 = 0.333… (block 3), 1/6 = 0.1666… (block 6), 2/3 = 0.666… (block 6). Test it by factoring the denominator: only factors of 2 and 5 give a terminating decimal, anything else repeats.
How do I reduce a fraction?
Divide both parts by their greatest common divisor. For 18/24 the GCD is 6, giving 3/4. This page reduces automatically and shows the working; after reduction the two parts are coprime, which is what "lowest terms" means.
Is any data uploaded?
No. All converting runs locally in the browser.
示例与注意事项Example & notes
一个例子A worked example
把 18/24 化简：填分子 18、分母 24，工具给出最简分数 3/4、小数 0.75、百分数 75%，并显示约分过程（最大公约数 6）。Reduce 18/24: enter 18 and 24 and you get 3/4, 0.75 and 75%, with the reduction shown (GCD 6).
注意事项Things to watch
- 分母为 0 时会直接报错，而不是给出无穷大。A zero denominator is reported as an error rather than producing infinity.
- 循环小数会标注循环节（如 1/3 → 0.333…，循环节 3），但小数位只保留到能区分循环节为止。Repeating decimals are flagged with their block (1/3 → 0.333…, block 3), with just enough decimal places to show it.
- 负号会跟随分子（−1/2 而不是 1/−2），符合中学书写习惯。The sign follows the numerator (−1/2 rather than 1/−2), matching school notation.
相关问答More Q&A
怎么快速判断一个分数是不是循环小数？How do I tell quickly whether a fraction repeats?
把分母分解质因数：只含 2 与 5 的因子（相乘的任意次幂）就是有限小数，如 8=2³、20=2²×5；只要还有别的质因数（如 3、6、7）就一定是循环小数。Factor the denominator: only factors of 2 and 5 in any powers (8=2³, 20=2²×5) give a terminating decimal; any other prime factor (3, 6, 7…) guarantees a repeating one.
为什么 0.75 可以写成 75%？Why is 0.75 the same as 75%?
百分数就是「百分之一」作单位：75% = 75/100 = 0.75。互转规则是乘 100 加 % 号（分数→百分数）、除 100 去 % 号（百分数→小数）。A percentage means "per hundred": 75% = 75/100 = 0.75. Multiply by 100 and add % going one way, divide by 100 and drop % going the other.