Q2 of 124 Page 1

Write down the decimal expansions of the following rational numbers by writing their denominators in the form, where m, n are non-negative integers.

(i) (ii)


(iii) (iv)


(v)

(i) = = the denominator is in the form of


⇒ = 0.375


(ii) = = the denominator is in the form of


⇒ = 0.104


(iii) = = the denominator is in the form of


⇒ = 0.0875


(iv) = = the denominator is in the form of


⇒ = 23.3408


(v) = = the denominator is in the form of


⇒ = 0.0004128


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If p, q are prime positive integers, prove that is an irrational number.

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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

(i) (ii)


(iii) (iv)


(v)

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What can you say about the prime factorizations of the denominators of the following rational?

(i) 43.123456789


(ii)


(iii)


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 1

State Euclid’s division lemma.