Recurring Decimal to Fraction Calculator

The Recurring decimal to fraction calculator is used to calculate how much a number written in repeating decimal digits can be written in fractions. This otherwise simple looking online calculator actually computes 6 steps to complete the conversion task.

Recurring Decimal to Fraction Calculator
Recurring Decimal to Fraction Calculator Results
The Number
Vulgar Fraction

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Recurring Decimal to Fraction Calculator: This image shows Recurring Decimal to Fraction formula and algorythms associated calculations used by the Recurring Decimal to Fraction Calculator

Everything You Need to Know about Recurring Decimal to Fraction Calculator

Any guesses how long it will take you to do all those calculations? Right, more than you think.

So, moving on, every calculation you make, the processor will do it way faster, giving you accurate results than you are capable of producing. However, given the fact that time is crucial and there are other tasks to perform too, iCalculator developed the recurring decimal to fraction calculator to help save you time.

What is recurring decimal to fraction conversion?

Before we start with the details of the decimal to fraction calculator, let's understand its function first. As mentioned in its name, this calculator computes the conversion of a recurring decimal number into its fractional equivalent.

To understand it better, suppose you need to find the fractional equivalent of, say, 0.333333

Recurring decimal to fraction conversion for single recurring digit

So, give it a name, say, x.


  • x = 0.333333----------(1)
  • 10x = 3.33333------(2)
  • Subtract (1) from (2)
  • 9x = 3
  • x = 3/9
  • x = 1/3

Thus, it is clear that 1/3 is the fractional equivalent of 0.333333

But no, this is the case for a single repeating digit after the decimal. What if you have a number with two recurring decimal digits, like, 0.21212121. In such a case,

Recurring decimal to fraction conversion for two recurring digits

x = 0.21212121---(1)

Now, we can't multiply both sides by 10 because that will change the order of the recurring decimals. So, we'll need to multiply both sides by 100. So, now we have,

100x = 21.212121---(2)

Now, subtract (1) from (2), and we'll have

  • 99x = 21
  • x = 21/99
  • x = 7/33

Recurring decimal to fraction conversion for three recurring digits

In a similar way, if the recurring decimal digits are in a set of three, you'll need to multiply both sides by 1000, for example, suppose

x = .738738738738

Keeping the above rule in mind,

  • 1000x = 738.738738738
  • 999x = 738
  • x = 738/999
  • x = 82/111

In simple words, to find the fractional equivalent of a recurring decimal number, you need to multiply both sides with 10's exponent whose exponential value is equal to the number of recurring digits.

However, if you have a single digit recurring decimal number such as 738.333333, then, how will you solve this? Sounds tricky? No, remember the rule. Just multiple 738.333333 with 10 and you'll have 7383.33333. It's the same journey now, right? No. That will give you the wrong answer.

Recurring decimal to mixed fraction conversion

That's because in such a case, the number to the left of the decimal point (or the number before the decimal point, whichever way you remember better) is kept aside. Then you work on the given fraction the way you will normally do.

So, working on 0.33333 will give you a fraction of 1/3. Now comes the twist of mixed fractions. The 738 you kept aside will be the reason it becomes a mixed fraction, and you'll have

x = 738⅓

To confirm, just multiply 738 by 3, add 1 to it and divide the sum by 3, and you'll have 738.33333.

In the end, it all boils down to how fast you are with simplifying fractions. And remember, there would've been no online calculators, or any other math calculator for that matter, if fraction simplification was so simple.

Uses of Recurring Decimal to Fraction Calculator in Real Life

From baking to banking to chemical experiments, this particular mathematical calculation plays an important role in all of them. Accounts, stats, engineering, recurring decimal to fraction conversion has found its usage in all walks of life. There's hardly any mathematical work where fractions are not included. And whenever you come across decimals, there's a high probability of you needing fractions for further calculations.


The magical world of math and decimals often takes you to a point where you need to transcend into the realm of fractions. And whenever that happens, you don't need to worry about going through all those calculation steps anymore, calculating math manually is a thing of the past. The recurring decimal to fraction calculator by iCalculator will do it for you, quickly and accurately.

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