Decimal Calculator — Fraction ↔ Decimal Converter
Convert any fraction to its decimal form — terminating or repeating — or convert a decimal back to a simplified fraction, with step-by-step working shown for each conversion.
Conversion mode
Non-terminating repeating — repeating block: (3)
Kā darbojas šis kalkulators?
To convert fraction p/q to decimal: divide by long division; it terminates iff q's only prime factors are 2 and 5. To convert a terminating decimal to a fraction: write as integer / 10^(decimal places), then divide by GCD. Step-by-step working is shown for both directions.
Formula
How this is calculated
A fraction p/q converts to a decimal by performing long division of p by q. Whether the result terminates or repeats depends entirely on the denominator (after simplification): if q's only prime factors are 2 and 5, the decimal terminates (e.g. 1/4 = 0.25); otherwise, remainders must eventually repeat, producing a repeating decimal (e.g. 1/3 = 0.333…). This calculator tracks each remainder during long division — when a remainder is seen a second time, the repeating block has been found. The period (length of the repeating part) divides φ(q), Euler's totient of the denominator.
Converting a terminating decimal to a fraction is straightforward: a decimal with d places equals the integer part divided by 10^d. For example, 0.625 = 625/1000. The fraction is then simplified using the greatest common divisor (GCD) of numerator and denominator, found with the Euclidean algorithm, giving 5/8.
Repeating decimals require a different approach to convert back: multiply the decimal by 10^(period) to shift one full cycle, then subtract the original to eliminate the repeating tail and solve for the fraction. This calculator handles the terminating case directly; for repeating-to-fraction conversion, enter the rounded decimal or work out the algebraic form by hand.
Biežāk uzdotie jautājumi
After simplifying the fraction, look at the denominator. If its only prime factors are 2 and 5 (e.g. 4, 5, 8, 10, 20, 25), the decimal terminates. Any other prime factor (3, 7, 11, 13, …) causes the decimal to repeat.
The period is the number of digits in the repeating cycle. For example 1/7 = 0.142857142857… has a period of 6. The period is always less than the denominator and divides its Euler's totient.
The Decimal → Fraction mode works only for terminating decimals. To convert a repeating decimal like 0.3̄ = 1/3, set x = 0.333…, then 10x = 3.333…, subtract to get 9x = 3, so x = 1/3. Alternatively, enter the fraction (numerator/denominator) directly and the calculator will confirm the repeating form.
Pazīstams arī kā
TG we-Calculate Editorial Team. (2026). Decimal Calculator — Fraction ↔ Decimal Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/lv/calculator/decimal-calculator
TG we-Calculate Editorial Team. "Decimal Calculator — Fraction ↔ Decimal Converter." TG we-Calculate. 2026. https://we-calculate.com/lv/calculator/decimal-calculator.
TG we-Calculate Editorial Team, "Decimal Calculator — Fraction ↔ Decimal Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/lv/calculator/decimal-calculator
@misc{wecalculate_decimal_calculator, title = {Decimal Calculator — Fraction ↔ Decimal Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/lv/calculator/decimal-calculator}}, year = {2026}, note = {TG we-Calculate} }
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