What can the maximum number of digits be in the repeating block of digits in the decimal expansion of (1\over 17)? Perform the division to check your answer.

5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of (1over 17)? Perform the division to check your answer.

Number Systems

Exercise 1.3

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Class 9

Number Systems

Exercise 1.3

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

(i) (36over 100)                  

(ii) (1over 11)                       

(iii) (4{1over 8})                  

(iv) (3over 13)

(v) (2over 11)                      

(vi) (329over 400)

2. You know that ({1over 7}=0.overline{142857}). Can you predict what the decimal expansion of (2over 7), (3over 7), (4over 7), (5over 7), (6over 7) are without actually doing the long division? If so, how?

3. Express the following in the form (pover q), where p and q are integers and q ≠ 0.

(i) (0.overline{6})

(ii) (0.4overline{7})      

(iii) (0.overline{001})

4. Express 0.99999 …. in the form (pover q). Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of (1over 17)? Perform the division to check your answer.

6. Look at several examples of rational numbers in the form (pover q) (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?

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

8. Find three different irrational numbers between the rational numbers (5over 7) and (9over 11).

9. Classify the following numbers as rational or irrational:

(i) (sqrt{23})

(ii) (sqrt{225})

(iii) 0.3796

(iv) 7.478478…               

(v) 1.101001000100001…

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