Fraction to Decimal Calculator
Fraction to Decimal Calculator converts fractions into exact or repeating decimals, simplifies fractions, shows long-division steps, and displays rounding options.
0.n for numerator and d for denominator. Parsed with Math.js and shown exactly (no LaTeX).Results
n / dHelping notes
- Leave “Expression” empty to compute just
n / d. - Use
nanddinside the expression to reference Numerator and Denominator. - Uses Math.js BigNumber with 64‑digit precision for reliable results.
What is Fraction to Decimal Calculator
A Fraction to Decimal Calculator is a simple but powerful tool that converts a rational number given as a fraction into its decimal representation. It accepts proper fractions, improper fractions, and mixed numbers, and returns the decimal either exactly (when terminating or repeating) or numerically to a specified precision. The calculator also explains the conversion steps, shows long-division work, identifies repeating cycles, and can express repeating decimals with overline notation for clarity.
About the Fraction to Decimal Calculator
The tool relies on basic division: numerator ÷ denominator. For mixed numbers it first converts to an improper fraction:
Not all fractions produce terminating decimals. A fraction \(\dfrac{p}{q}\) (in lowest terms) has a terminating decimal expansion exactly when the denominator \(q\) has no prime factors other than 2 and 5. Otherwise the decimal repeats. The calculator detects this and either writes the repeating block with an overline, for example:
It can also present a rounded decimal to a user-specified number of decimal places, show the long-division table of remainders (so you can see how the repeat cycle appears), and simplify input fractions via gcd before conversion:
How to Use this Fraction to Decimal Calculator
- Enter the fraction as a/b, or as a mixed number (e.g., 3 1/4). The calculator will accept integers, negative values, and zero where appropriate.
- Optionally select whether you want the exact decimal (with repeating notation), a rounded decimal to N places, or the long-division steps shown.
- Click Convert — the calculator simplifies the fraction, performs division, and outputs the decimal result plus an explanation.
- If the decimal repeats, the tool highlights the repeating sequence and displays it with an overline; if it terminates, it confirms the denominator's prime factorization contains only 2 and/or 5.
- Use the long-division view to study remainders and repeat cycles: each remainder maps to the next digit, and a repeated remainder signals the start of a repeating block.
Examples
This Fraction to Decimal Calculator is ideal for students learning about decimals and rational numbers, teachers preparing examples, and anyone needing accurate conversions or clear long-division demonstrations. It’s a practical educational tool and a handy utility for arithmetic, finance, and programming tasks.