Question

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q?

(i) 43.123456789

Solution

left parenthesis straight i right parenthesis space 43.123456789 space space equals 43123456789 over 1000000000 space space space space space space space space space space space space space space space space space space space space space space space space space space equals 43123456789 over 10 to the power of 9 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 43123456789 over denominator 2 to the power of 9 cross times 5 to the power of 9 end fraction

∴ 43.123456789 is a rational number of the form p/q, where ‘p’ and ‘q’ are co-primes and the prime factors of ‘q’ are of the form 2ⁿ.5ⁿ, where n is nonnegative integer.

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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Real Numbers

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q?

(i) 43.123456789

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

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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For Daily Free Study Material Join wiredfaculty

Real Numbers

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q?(i) 43.123456789

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q?

(i) 43.123456789