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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 Kalkulator does all three steps automatically and shows the Wynik in lowest terms.
Common Decimal to Fraction Equivalents
| 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.
Często Zadawane Pytania
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.
Can all decimals be expressed as fractions?
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.