Q1 of 124 Page 1

State Euclid’s division lemma.

Euclid’s Division Lemma: Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b. (It is a technique to compute the Highest Common Factor (HCF) of two given positive integers.)


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2

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)

3

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

(i) 43.123456789


(ii)


(iii)


(iv) 0.120120012000120000…

 2

State Fundamental Theorem of Arithmetic.

 3

Write 98 as product of its prime factors.