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Real Numbers

Question

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

$left parenthesis vii right parenthesis space space fraction numerator 129 over denominator 2 squared 5 to the power of 7 7 to the power of 5 end fraction$

Solution

space space left parenthesis v i i right parenthesis space space fraction numerator 129 over denominator 2 squared 5 to the power of 7 7 to the power of 5 end fraction rightwards double arrow

has a non-terminating repeating decimal expansion.

[By NCERT Theorem 1.7]

Some More Questions From Real Numbers Chapter

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Express each number as a product of its prime factors: (i) 140

Express each number as a product of its prime factors: (ii) 156

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005

Express each number as a product of its prime factors: (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

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Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (iii) 336 and 54

Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21

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