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…

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

Solved Example on Recurring Decimal

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.

Related Terms for Recurring Decimal

  • Decimal
  • Digit
  • Nonrepeating Decimal
  • Recurring Decimal
  • Repeating Decimal
  • Sequence