About Repeating Decimal Calculator
This repeating decimal calculator divides one number by another, stops as soon as a remainder repeats, and marks the repeating block and its length. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 1 ÷ 7, which gives 0.(142857): the six digits 142857 repeat forever, so the period is 6. The remainders 1, 3, 2, 6, 4, 5 cycle through every non-zero value less than 7, which is why the period is as long as it can be.
Other examples: 5 ÷ 13 = 0.(384615) and 7 ÷ 12 = 0.58(3), where only the 3 repeats after a non-repeating start. A fraction in lowest terms has an ending decimal only if its denominator has no prime factors except 2 and 5.
How to use Repeating Decimal Calculator
- Choose With remainder, With decimals or Polynomials.
- Type the dividend (the number being divided) and the divisor (the number you divide by).
- In decimal mode, choose how many decimal places you want at most.
- Read the quotient and remainder at the top, then follow the drawn layout below.
- Open the steps to see each digit: divide, multiply, subtract, bring down. The check line multiplies back to confirm.
Features
- The classic bracket layout, drawn with real columns and lines.
- Quotient and remainder for whole numbers, with the mixed-number form.
- Decimal expansion that stops when it ends or repeats, with the repeating block marked.
- Decimal dividends and divisors, with the decimal point shifted for you.
- Polynomial long division with exact fractions and the quotient plus remainder form.
- Step-by-step list and a multiplication check.
- Negative numbers and rounded results for long periods.
Why decimals repeat
There are only (d - 1) possible non-zero remainders when dividing by d, so one must repeat within d steps, and then the digits repeat.
period of 1/p divides p - 1 for a prime p other than 2 and 5Worked examples
1 ÷ 7 gives 0.(142857)
Period 6.
5 ÷ 13 gives 0.(384615)
Period 6 as well.
7 ÷ 12 gives 0.58(3)
A non-repeating 58, then 3 repeats.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- If the remainder is not zero when the digits run out, either write it as a remainder or put a decimal point and keep adding zeros.
- A decimal ends only if the divisor, in lowest terms, has no prime factors other than 2 and 5.
- To check any answer, multiply the quotient by the divisor and add the remainder. You should get the dividend.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I find the repeating part of a decimal?
Do the long division and watch the remainders. When a remainder appears a second time, the digits between the two appearances are the repeating block.
Which fractions have ending decimals?
Those whose denominator, in lowest terms, has only 2 and 5 as prime factors. Every other fraction gives a repeating decimal.
More Long Division Calculator pages
- Long Division CalculatorEnter a dividend and a divisor to see the long division drawn out, with the quotient, the remainder and every step.
- Long Division With RemaindersEnter two whole numbers to get the quotient and remainder, with the layout drawn out.
- Long Division With DecimalsDivide decimals or carry the division on past the point, with every step drawn.
- Polynomial Long Division CalculatorEnter two polynomials to divide, with the layout drawn out term by term.