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Exercise 1.3

Q.1:Write the following in decimal form and say what kind of decimal expansion each has:

i36100= 0.36 

ii111= 0.09090909 =0.09

iii338= 4.125 

iv313= 0.230769230769 = 0 .230769

v 211= 0.181818181818 = 0.18 

vi 329400= 0.8225 

Q.2. You know that 17 = 0.142857. Can you predict what the decimal expansion of 27,37,47,57,67 are without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of 17 carefully.]

Q.3. Express the following in the form pq where p and q are integers and q ≠ 0.

(i) 0.6 (ii) 0.47 (iii) 0.001

Q.4. Express 0.99999…in the form pq. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Q.5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.

Q.6. Look at several examples of rational numbers in the form pq (q≠0) where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Q.7. Write three numbers whose decimal expansions are non-terminating non-recurring.

Q.8. Find three different irrational numbers between the rational numbers 57 and 911.

Q.9. Classify the following numbers as rational or irrational:

(i) 23 (ii) 225 (iii) 0.3796

(iv) 7.478478… (v) 1.101001000100001…