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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