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# Recurring Decimal

## Definition of Recurring Decimal

Recurring Decimals are decimals in which a digit or a sequence of digits keeps repeating. For example: 0.666666666… .

• Recurring decimal is also known as repeating decimal.
• The repeating decimal can be represented by putting a bar over the digit or the sequence of digits that repeat. For instance, 0.166666666 can also be written as .

### Examples of Recurring Decimal

Here are a few examples of recurring or repeating decimals.
0.3333333 or
0.166666666 or
0.86666666666 or

### Solved Example on Recurring Decimal

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D.

#### Solution:

Step 1: When a digit or sequence of digits keeps repeating in a decimal, it is called a repeating decimal.
Step 2: For , when 8 is divided by 5, the quotient is 1.6
Step 3:For , when 1 is divided by 4, the quotient is 0.25.
Step 4: For , when 5 is divided by 10, the quotient is 0.5.
Step 5: For , when 1 is divided by 11, the quotient is 0.090909... and the digits 09 are repeating. Step 6: Therefore, is a repeating decimal.

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