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

= 1.666........

For, 5/3 when 5 is divided by 3, the quotient is

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

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

**Therefore, 5/3 is a pure recurring decimal.**

**(b)** 1/37

= 0.027027........

For, 1/37 when 1 is divided by 37, the quotient is

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

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

**Therefore, 1/37 is a pure recurring decimal.**

**(c)** 9/37

= 0.243243......

For, 9/37 when 9 is divided by 37, the quotient is

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

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

**Therefore, 9/37 is a pure recurring decimal.**

● **Related Concept **

● Decimals

● Conversion of Unlike Decimals to Like Decimals

● Decimal and Fractional Expansion

● Converting Decimals to Fractions

● Converting Fractions to Decimals

● H.C.F. and L.C.M. of Decimals

● Repeating or Recurring Decimal

● BODMAS/PEMDAS Rules - Involving Decimals

● PEMDAS Rules - Involving Integers

● PEMDAS Rules - Involving Decimals

● BODMAS Rules - Involving Integers

● Conversion of Pure Recurring Decimal into Vulgar Fraction

● Conversion of Mixed Recurring Decimals into Vulgar Fractions

● Rounding Decimals to the Nearest Whole Number

● Rounding Decimals to the Nearest Tenths

● Rounding Decimals to the Nearest Hundredths

● 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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