BYTETOOLS

Fraction to Decimal Converter

Convert any fraction to its exact decimal form, including repeating decimals like 1/7 = 0.(142857). See the repeating block and period instantly.

Repeating
Decimal type
6 digits
Repeating period
0.142857142857
Decimal (approx.)

Exact decimal

1/7 = 0.(142857)

The digits in parentheses repeat forever. The block was found by long division — the moment a remainder appears twice, the digits between its two appearances must cycle.

What is the Fraction to Decimal Converter?

The ByteTools Fraction to Decimal Converter turns any fraction into its exact decimal representation.

  • Exact decimal expansion with repeating-block detection
  • Shows the period (length of the repeating block)
  • Classifies decimals as terminating, repeating or whole
  • Handles negative fractions and improper fractions
  • Rounded decimal approximation alongside the exact form
  • 100% private — runs entirely in your browser

How to use the Fraction to Decimal Converter

  1. 1

    Enter the numerator (top number) of the fraction.

  2. 2

    Enter the denominator (bottom number).

  3. 3

    Read the exact decimal — repeating digits are shown in parentheses.

  4. 4

    Check whether the decimal terminates or repeats, and the period length.

  5. 5

    Click Copy to grab the result.

About the Fraction to Decimal Converter

The ByteTools Fraction to Decimal Converter turns any fraction into its exact decimal representation. Unlike a plain calculator, it detects repeating decimals: 1/7 becomes 0.(142857), where the digits in parentheses repeat forever. It also tells you whether the decimal terminates, how long the repeating block is, and gives a rounded approximation.

It works by performing long division and recording the position of every remainder. The moment a remainder appears a second time, the digits between its two appearances must cycle — that is the repeating block. This is the same method taught in school, just automated, so students can check homework and teachers can generate examples.

Everything runs 100% locally in your browser with JavaScript. Nothing is uploaded or stored, so the converter is instant, private and works offline. Copy the exact decimal with one click.

Frequently asked questions

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 5/8 = 5 ÷ 8 = 0.625. Some fractions divide evenly (terminating decimals), while others produce digits that repeat forever, like 1/3 = 0.333… This tool does the division and shows the exact result either way.

What is a repeating decimal?

A repeating decimal has a block of digits that cycles forever, such as 1/7 = 0.142857142857… The repeating block is usually written in parentheses or with a bar: 0.(142857). Every fraction produces either a terminating or a repeating decimal — never a random unending one.

How do you know if a fraction terminates or repeats?

Reduce the fraction fully, then look at the denominator's prime factors. If they are only 2s and 5s, the decimal terminates (like 3/40). Any other prime factor forces a repeating decimal (like 1/6 = 0.1666…, because of the factor 3).

How does the tool find the repeating block?

It performs long division and remembers the position of each remainder. When a remainder shows up a second time, the digits generated between the two appearances must repeat forever, because the division is back in exactly the same state. That block is the repeating period.

How long can the repeating block be?

At most one less than the denominator. For example, 1/7 has a 6-digit block and 1/17 has a 16-digit block. Fractions whose repeating block hits this maximum are called full reptend primes — 7, 17, 19, 23 are famous examples.

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