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Question

# Which of the following rational numbers have terminating decimal? (i) $\frac{16}{225}$ (ii) $\frac{5}{18}$ (iii) $\frac{2}{21}$ (iv) $\frac{7}{250}$ (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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