Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Worksheet - 2: Number System

Class 9 Maths Number System CBSE Worksheets- 2

Q.1. What is the value of (23)2?
Solution: 
(23)2 = 23x2           [∵ (xm)n = xm.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:

Class 9 Maths Number System CBSE Worksheets- 2

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)

\piπ: 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)

\piπ: 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.

Class 9 Maths Number System CBSE Worksheets- 2


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?
Class 9 Maths Number System CBSE Worksheets- 2
Class 9 Maths Number System CBSE Worksheets- 2
Class 9 Maths Number System CBSE Worksheets- 2

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

Class 9 Maths Number System CBSE Worksheets- 2

The document Class 9 Maths Number System CBSE Worksheets- 2 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Number System CBSE Worksheets- 2

1. What is the number system?
Ans. The number system is a way of representing and expressing numbers using symbols or digits. It includes different types of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. These numbers are organized in a systematic manner, allowing us to perform various mathematical operations and calculations.
2. What are natural numbers?
Ans. Natural numbers are a set of positive integers starting from 1 and going up to infinity. They are denoted by the symbol 'N'. In simple terms, natural numbers are the counting numbers used to represent the quantity of objects or entities. For example, 1, 2, 3, 4, 5, and so on are natural numbers.
3. What is the difference between whole numbers and natural numbers?
Ans. The main difference between whole numbers and natural numbers is that whole numbers include zero (0) along with all the positive integers, while natural numbers only consist of positive integers. In other words, the set of natural numbers is a subset of the set of whole numbers. For example, 0, 1, 2, 3, 4, 5, and so on are whole numbers, whereas 1, 2, 3, 4, 5, and so on are natural numbers.
4. How are rational numbers represented?
Ans. Rational numbers are represented in the form of fractions, where both the numerator and the denominator are integers. These fractions can be written in the form p/q, where 'p' and 'q' are integers and 'q' is not equal to zero. Rational numbers include both terminating and non-terminating repeating decimals. For example, 1/2, 3/4, 5/8, and 2/3 are rational numbers.
5. What are irrational numbers?
Ans. Irrational numbers are numbers that cannot be expressed as fractions or ratios of two integers. They are non-repeating and non-terminating decimals. Irrational numbers include values such as √2, π (pi), and e (Euler's number). These numbers are represented by symbols or decimal approximations since their exact values cannot be expressed using a finite number of digits.
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