Repeating or Recurring Decimal
Definition of Recurring Decimal:
Recurring decimal is also known as repeating decimal. In a decimal, a digit or a sequence of digits in the decimal part keeps repeating itself infinitely. Such decimals are called non-terminating repeating decimals or recurring decimals.
More information about Repeating or Recurring Decimal:
● The repeating decimal can be expressed by putting a bar over the digit or on the repeated digits that repeat itself.
● Also, dot can be put over the first and the last digit of the repeated block.
A few worked-out problems are explained here with step-by-step explanation to understand how to calculate or find repeating or recurring decimal.
Examples of Recurring Decimal:
(a) 17/45
= 0.3777…….
For, 17/45 when 17 is divided by 45, the quotient is 0.3777.... and the digit 7 is repeating.
For instance, 0.377777777777......... can also be written as 0.37
Alternatively, we can write it by placing a dot above the repeating digit 7 in the quotient.
Therefore, 17/45 is a repeating decimal.
(b) 1/3
= 0.333.........
For, 1/3 when 1 is divided by 3, the quotient is 0.333..... and the digit 3 is repeating.
For instance, 0.33333333......... can also be written as 0.3
Alternatively, we can write it by placing a dot above the repeating digit 3 in the quotient.
Therefore, 1/3 is a repeating decimal.
(c) 2/11
= 0.1818
For, 2/11 when 2 is divided by 11, the quotient is 0.1818..... and the digits 18 are repeating.
For instance, 0.181818......... can also be written as 0.18
Alternatively, we can write it by placing a dot above the repeating digits 18 in the quotient.
Therefore, 2/11 is a repeating decimal.
● Related Concept
● Decimals
● Conversion of Unlike Decimals to Like Decimals
● Decimal and Fractional Expansion
● Converting Decimals to Fractions
● Converting Fractions to Decimals
● H.C.F. and L.C.M. of Decimals
● Repeating or Recurring Decimal
● Conversion of Pure Recurring Decimal into Vulgar Fraction
● Conversion of Mixed Recurring Decimals into Vulgar Fractions
7th Grade Math Problems
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