Are you in a dilemma on the concept of Pure Recurring Decimals? If so, you will get a complete grip on Pure Recurring Decimals such as Definition, Examples, Procedure on How to Identify a Pure Recurring Decimal. Furthermore, refer to the solved examples on Pure Recurring Decimals for a better idea of the concept.

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## Pure Recurring Decimal – Definition

A Decimal in which all the digits in the decimal part are repeated is called a Pure Recurring Decimal.

For Example: When 5/3 is divided the quotient is 1.6666…. and all the digits in the decimal part repeat continuously it is called a Pure Recurring Decimal.

### How to Identify a Pure Recurring Decimal?

Follow the simple guidelines on how to identify a pure recurring decimal. They are in the following fashion

- Firstly, divide the numerator with the denominator from the given fraction.
- After dividing if you get to see all the digits in the decimal part repeat infinitely then it is called a pure recurring decimal.

For a better understanding of the concept of Pure Recurring Decimals check out few worked-out examples provided in the later sections.

### Pure Recurring Decimal Examples

1. Is \(\frac { 5 }{ 3 } \) a Pure Recurring Decimal?

Solution:

Simply divide the numerator 5 with denominator 3. Check for if all the digits in the decimal part repeat or not after performing the division process. Simply place a bar on the repeating digits itself.

\(\frac { 5 }{ 3 } \) = 1.66666……

Thus, \(\frac { 5 }{ 3 } \) expressed in decimal form is 1.6666…. or 1.\(\overline{6}\)

1.6666…. is called a Pure Recurring Decimal as it has all the digits after the decimal part repeating.

2. Is \(\frac { 7 }{ 3 } \) a Pure Recurring Decimal?

Solution:

Simply divide the numerator 7 with denominator 3. Check for if all the digits in the decimal part repeat or not after performing the division process. Simply place a bar on the repeating digits itself.

\(\frac { 7 }{ 3 } \) = 2.333333……

Thus, \(\frac { 7 }{ 3 } \) expressed in decimal form is 2.3333…. or 2.\(\overline{3}\)

2.3333…. is called a Pure Recurring Decimal as it has all the digits after the decimal part repeating.

### FAQs on Pure Recurring Decimals

**1. What is a Pure Recurring Decimal?**

A Decimal in which all the digits after the decimal point repeat is called a Pure Recurring Decimal.

**2. How to Determine a Pure Recurring Decimal?**

Just divide the numerator with the denominator and check if all the digits of the decimal part repeat or not. If the digits repeat then it is said to be a pure recurring decimal.

**3. Is 1/3 a Pure Recurring Decimal?**

Yes, 1/3 expressed in decimal form is 0.3333…. as it has all the digits in the decimal part repeat continuously.