Class 9 Maths Number System CBSE Worksheets- 2

Q.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

Q.2. What is the value of (625) ^1/4 ?
Solution:

Q.3. Which of the following are irrational numbers?
√3, √4, √5, 22/7, π, 0 
Solution:  √3, √5 and π are irrational numbers.

√3: Irrational (cannot be expressed as a fraction of two integers)

√4: Rational (equals 2, which is an integer)

√5: Irrational (cannot be expressed as a fraction of two integers)

22/7: Rational (a fraction of two integers)

$\backslash pi$π: Irrational (cannot be expressed as a fraction of two integers)

0: Rational (can be expressed as 0/1)

Q.4. Which of the following are rational?
2√3, 1, 0, 3.14, π, 22/7

Solution: 1, 0, 3.14 and 22/7 are rational numbers.

2√3: Irrational (product of a rational and an irrational number)

1: Rational (an integer, can be expressed as 1/1)

0: Rational (can be expressed as 0/1)

3.14: Rational (a terminating decimal, can be expressed as 314/100)

$\backslash pi$π: Irrational (cannot be expressed as a fraction of two integers)

22/7: Rational (a fraction of two integers)

Q.5. Which of the following cube roots is not irrational?
3 √5, 3√6, 3√7, 3√8, 3√9
Solution:  3√8 is not an irrational number.

Q.6. Which three integers are equal to their own cube roots?
Solution: –1, 0 and 1

[∵ 3√-1 = -1, 3√1 = 1 and 3√0 = 0 ]  

Q.7. Is the following number rational or irrational? 0.0769230769230769230...
Solution:
The given number is rational.  

The number 0.076923076923076923... is a repeating decimal. The number is rational because it has a repeating pattern and can be expressed as a fraction of two integers.

Q.8. Is 0.666 ...a “non-terminating rational” or “non-terminating recurring rational number”?
Solution: Non-terminating rational number.

0.666... (where the 6 repeats indefinitely) is a repeating decimal. It is a non-terminating recurring rational number because it has a repeating pattern and can be expressed as a fraction (specifically, 2/3).

Q.9. Is 1.27 27 27 ... non-terminating recurring or non-terminating non-recurring number?
Solution: It is a non-terminating recurring rational number.

1.272727... (where 27 repeats indefinitely) is a repeating decimal. It is a non-terminating recurring rational number because it has a repeating pattern and can be expressed as a fraction.

Q.10. The decimal representation of √3 is 1.73205807... . Is it non-terminating nonrecurring?
Solution: Yes

The decimal representation of √3 does not repeat and does not terminate.

Q.11. Is the product of a rational and an irrational number, rational?
Solution: No. It is an irrational number.

Q.12. Write the smallest non-negative integer.
 Solution: The smallest non-negative integer is ‘0’.

Q.13. Write the smallest positive integer.
Solution: The smallest positive integer is '1'.

Q.14. Up to how many decimal places, π and 22/7  are same?
Solution: π and 22/7 are same only up to 2 decimal places.

[∵ 22/7  = 3.142857142... and π =3.141592653589...]

Q.15. Which of the following is irrational?

Solution: √7 is irrational.

Q.16. Which of the following is the value of 0.999... expressed as p/q : 
(i) 9/10
(ii)  1
(iii)   999/1000
Solution:(ii) = 1