Math July 13, 2026 · 8 Min Read

Decimal Calculator – Guide & Formulas

Convert fractions to decimals, identify repeating patterns, and perform decimal arithmetic. Shows terminating vs repeating decimals with precision control.

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Put these formulas into practice with our instant, step-by-step Decimal Calculator.

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Convert fractions to decimals and identify repeating patterns instantly. Enter a fraction to see its decimal form, whether it terminates or repeats, and the repeating notation.

Key Takeaway

Use the free Decimal Calculator to convert fractions to decimals, identify repeating patterns, and perform decimal arithmetic. shows terminating vs repeating decimals with precision control. Get instant results with step-by-step explanations.

How to Use the Decimal Calculator

  1. Enter the numerator and denominator of the fraction.
  2. Review the decimal conversion result.
  3. Check whether the decimal terminates or repeats, and see the repeating notation if applicable.
  4. Adjust the precision (number of decimal places) to control output accuracy.

The Formula

To convert a fraction to decimal: divide the numerator by the denominator. A fraction a/b terminates if and only if the prime factorization of b contains only 2s and 5s.

Variable Definitions

  • Numerator: The top number of the fraction
  • Denominator: The bottom number of the fraction (cannot be zero)
  • Terminating Decimal: A decimal that ends (e.g., 0.5, 0.25) — the denominator has only factors of 2 and 5
  • Repeating Decimal: A decimal with a repeating pattern (e.g., 0.333..., 0.142857142857...)
  • Period: The length of the repeating block in a repeating decimal

Converting 7/12 to Decimal

Find the decimal representation of 7 divided by 12.

  1. Step 1: Set up the division: 7 ÷ 12.
  2. Step 2: 7 ÷ 12 = 0.583333... The 3 repeats infinitely.
  3. Step 3: Identify the repeating block: "3" has a period of 1.
  4. Step 4: Write in repeating notation: 7/12 = 0.583̄ or 0.58(3).
  5. Step 5: Verify: 0.58333... × 12 = 6.999... ≈ 7 —

Frequently Asked Questions