Pure Recurring Decimal

Definition of Pure recurring decimal:

A decimal in which all the digits in the decimal part are repeated is called a pure recurring decimal.

A few solved problems are explained step-by-step with detailed explanation.

Worked-out example of pure recurring decimal:

(a) 5/3

Pure recurring Decimal











= 1.666........



For, 5/3 when 5 is divided by 3, the quotient is 1.666.... and the digit 6 is repeating.

For instance, 1.666666 ......... can also be written as 1.6

Alternatively, we can write it by placing a dot above the repeating digit 6 in the quotient.

Pure Recurring



Therefore, 5/3 is a pure recurring decimal.



(b) 1/37

Example of Pure Recurring Decimal













= 0.027027........
For, 1/37 when 1 is divided by 37, the quotient is 0.027027.... and the digits 027 are repeating.

For instance, 0.027027........ can also be written as 0.027

Alternatively, we can write it by placing a dot above the repeating digits 027 in the quotient.

Pure Recurring Decimal Notation



Therefore, 1/37 is a pure recurring decimal.



(c) 9/37

Worked-out Example of Pure Recurring Decimals














= 0.243243......
For, 9/37 when 9 is divided by 37, the quotient is 0.243243....and the digits 243 are repeating.

For instance, 0.243243....... can also be written as 0.243

Alternatively, we can write it by placing a dot above the repeating digits 243 in the quotient.

Recurring Decimal Image



Therefore, 9/37 is a pure recurring 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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