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Question

Which of the following rational numbers have terminating decimal?

(i) 16225
(ii) 518
(iii) 221
(iv) 7250

(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iii)
(d) (i) and (iv)

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Solution

(i) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(ii) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iii) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iv) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is of the form, where m and n are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.

Then, x has a decimal expression which will have terminating decimal after 3 places of decimal.

Hence the (iv) option will have terminating decimal expansion.

There is no correct option.


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