소수에서 분수로 변환 계산기
임의의 소수를 약분된 분수로 변환합니다. 단계별 과정을 보여줍니다.
How to Convert a Decimal to a Fraction
To convert a decimal to a fraction:
- Count the decimal places (e.g., 0.75 has 2 decimal places)
- Write the decimal as a fraction over 10^n (e.g., 75/100)
- Simplify using the Greatest Common Divisor (GCD) → 75/100 = 3/4
Our calculator does all three steps automatically and shows the result in lowest terms.
일반적인 소수를 분수로 변환
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.125 | 1/8 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.5 | 1/2 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
What is the GCD?
The Greatest Common Divisor (GCD) is the largest number that divides both the numerator and denominator without remainder. Dividing both by the GCD simplifies the fraction to its lowest terms.
For example, GCD(75, 100) = 25. So 75/100 ÷ 25/25 = 3/4. The Euclidean algorithm is the standard efficient method: GCD(a, b) = GCD(b, a mod b) until b = 0.
자주 묻는 질문
How do I convert a repeating decimal to a fraction?
For a repeating decimal like 0.333..., set x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. For 0.142857142857... (repeating 6 digits), the process requires multiplying by 10^6.
What is the fraction for 0.625?
0.625 = 625/1000. GCD(625, 1000) = 125. So 625/1000 ÷ 125/125 = 5/8. Therefore 0.625 = 5/8.
모든 소수를 분수로 표현할 수 있나?
Terminating decimals (like 0.75) and repeating decimals (like 0.333...) can always be written as fractions. Non-repeating, non-terminating decimals (like π = 3.14159...) are irrational and cannot be expressed as exact fractions.