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.

$Recurring Decimal Image$