Fraction to Decimal Calculator
Enter a numerator and denominator to convert a fraction to its decimal form. See whether it terminates or repeats, and get full long division steps.
Why Some Fractions Repeat
A fraction p/q (in lowest terms) produces a terminating decimal if and only if the denominator q has no prime factors other than 2 and 5. Otherwise the decimal repeats. The length of the repeating block divides φ(q).
Frequently Asked Questions
Divide the numerator by the denominator using long division. The result is the decimal representation. For example, 3 ÷ 4 = 0.75.
If the denominator (in lowest terms) has any prime factors other than 2 and 5, the decimal will repeat. For example, 1/3 repeats because 3 is prime and not 2 or 5.
A bar (vinculum) is placed over the repeating block. For example, 1/3 = 0.3̄ and 1/7 = 0.142857̄. This indicates those digits repeat infinitely.
For 1/n, the repeating block length is at most n−1 digits. For example, 1/7 has a 6-digit repeating block: 142857.
Yes, mathematically 0.999... = 1. This can be shown by the fraction 1/1 = 1, and also: let x = 0.999..., then 10x = 9.999..., so 9x = 9, thus x = 1.
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