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

Decimals

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

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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