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

Recurring Decimals

= 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.

Repeating Decimal Sign

Therefore, 17/45 is a repeating decimal.

(b) 1/3

Repeating Decimals

= 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.

Repeating Decimal Notation

Therefore, 1/3 is a repeating decimal.

(c) 2/11

Examples of Recurring Decimal

= 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.

Recurring Decimal Notation

Therefore, 2/11 is a repeating decimal.

Related Concept


Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed 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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