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
= 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.
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 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.
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 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.
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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