Very Short Answers - Number System Class 9 Notes | EduRev

Ques 1. What is the value of (23)²?
 Solution: (2³)² =2^3x2                                       [∵ (x^m)ⁿ = x^m.n]
=2⁶
=2 x 2 x 2 x 2 x 2 x 2 = 64
Ques 2. What is the value of 
Solution:

  Ques 3. Which of the following are irrational numbers? 

Solution:  and π are irrational numbers.
Ques 4. Which of the following are rational?

Solution: 1, 0, 3.14 and  are rational numbers.
Ques 5. Which of the following cube roots is not irrational?

Solution: is not an irrational number.                                                        

Ques 6. Which three integers are equal to their own cube roots?
Solution: –1, 0 and 1                                                                            
Ques 7. Is the following number rational or irrational? 0.0769230769230769230...
Solution: The given number is rational.               [∵ “076923” repeats]
Ques 8. Is 0.666 ...a “non-terminating rational” or “non-terminating recurring rational number”?
Solution: Non-terminating rational number.
Ques 9. Is 1.27 27 27 ... non-terminating recurring or non-terminating non-recurring number?
Solution: It is a non-terminating recurring rational number.
Ques 10. The decimal representation of  is 1.73205807... . Is it non-terminating nonrecurring?
Solution: Yes
Ques 11. Is the product of a rational and an irrational number, rational?
Solution: No. It is an irrational number.
 Ques 12. Write the smallest non-negative integer.
 Solution: ‘0’ Question
13. Write the smallest positive integer.
 Solution: 1 Question 
14. Up to how many decimal places, π and   are same?
Solution: π and  are same only up to 2 decimal places.
[∵  = 3.142857142... and π =3.141592653589...]
Ques 15. Which of the following is irrational?

Solution:  is irrational.

Ques 16. Which of the following is the value of 0.999... expressed as p/q : 
(i) 9/10       (ii)  1      (iii)   999/1000
Solution: 0.999... = 1
Ques 17. What is a terminating decimal?
Solution: The number with a finite decimal part are known as terminating decimal.
Example: 0.375 is a terminating decimal.
Note: If we express a rational number as a decimal number and remainder becomes zero after certain stage, then the decimal expansion is terminating.