Q3 of 54 Page 12

Write the following rationales in decimal form using Theorem 1.1.

(i)


(ii)


(iii)


(iv)


(v)

According to Euclid’s Division Algorithm,


For any two positive integers, ‘a’ and ‘b’, there exists a unique pair of integers ‘q’ and ‘r’ which satisfy the relation:


a = bq + r , 0 ≤ r ≤ b


(i)






(ii)







(iii)





(iv)






(v)






More from this chapter

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2

Without performing division, state whether the following rational numbers will have a terminating decimal form or non-terminating, repeating decimal form.

 2

Without performing division, state whether the following rational numbers will have a terminating decimal form or non-terminating, repeating decimal form.

 4

The decimal form of some real numbers is given below. In each case, decide whether the number is rational or not. If it is rational, and expressed in form what can you say about the prime factors of q?

(i) 43.123456789


(ii) 0.120120012000120000….


(iii) 43.

 1

Prove that the following are irrational.