Recurring Decimal

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Definition of Recurring Decimal

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

More about Recurring Decimal

  • 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

Video Examples: Recurring Decimals


Solved Example on Recurring Decimal

Ques: Which of the following is a repeating decimal?.

    Choices:
    A.
    B.
    C.
    D.
    Correct Answer: 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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