Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Worksheet - 1: Number System

Class 9 Maths - Number System CBSE Worksheets- 1

Q.1. Which of the following is an irrational number?
(a) 

Class 9 Maths - Number System CBSE Worksheets- 1
(b) √3
(c) 1/2
(d) 

Class 9 Maths - Number System CBSE Worksheets- 1
Ans.

An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation. Let's evaluate the options:

(a) √49/64: This is a rational number because both the numerator and denominator are perfect squares, and their square root can be expressed as a fraction of integers. √49/64 = 7/8.

(b) √3: This is an irrational number because the square root of 3 cannot be expressed as a fraction of integers, and its decimal representation goes on infinitely without repeating.

(c) 1/2: This is a rational number because it can be expressed as a fraction of integers.

(d) -√1/4: This is a rational number because √1/4 = 1/2, and the negative sign only changes the sign of the rational number.

So, the irrational number among the given options is: (b) √3

Q.2. The numberClass 9 Maths - Number System CBSE Worksheets- 1in p/q form is
(a) 267/1000
(b) 26/10
(c) 241/900
(d) 241/999
Ans.
(c)
Solution:
let x be the p/q form, x =Class 9 Maths - Number System CBSE Worksheets- 1
multiply both side by 100,
100 x = Class 9 Maths - Number System CBSE Worksheets- 1 ...(i)
multiply both side by 10
1000 x = Class 9 Maths - Number System CBSE Worksheets- 1 ....(ii)
Subtract (ii) - (i)
1000 x - 100 x = Class 9 Maths - Number System CBSE Worksheets- 1
900 x = 241
⇒ x = 241/900
Hence, option (c) is correct

Question for Worksheet - 1: Number System
Try yourself:Q3: Every point on the number line represents, which of the following numbers?
View Solution

Q.4. The decimal representation of a rational number is either:

(a) Terminating or repeating

(b) Non-terminating and non-repeating

(c) Only terminating

(d) Only repeating

Ans: (a) Terminating or repeating

  •  A rational number is any number that can be expressed as a fraction pq\frac{p}{q}, where p and q are integers and q0q \neq 0
  • A terminating decimal is one that has a finite number of digits after the decimal point. 

  • A repeating decimal is one where a block of digits repeats infinitely.

Q.5. Insert 3 irrational number between 2.6 and 3.8
Ans. 
2.6 and 3.8
Irrational numbers are non repeating non - terminating
2.61010010001.....
2.802002000200002......
3.604004000400004.......

Q.6. What is the decimal form of the following no's.
(a) 18/11
(b) 3/26
(c) 1/17
(d) 2/13
Ans.
(a) 18/11 = 1.63636363...
(b) 3/26 = 0.11538461538
(c) 1/17 = 0.05882352941
(d) 2/13 = 0.15384615384

Q.8. Simplify: 
Class 9 Maths - Number System CBSE Worksheets- 1
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1

Q.9. Rationalise: 
Class 9 Maths - Number System CBSE Worksheets- 1
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1

Q.10. Find the value of 
Class 9 Maths - Number System CBSE Worksheets- 1
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
= 5+4 - 4√5 - 5 - 4 -  4√5  = -8√5

Q.11. If Class 9 Maths - Number System CBSE Worksheets- 1,
find the value of a & b.
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1
Rationalising LHS
Class 9 Maths - Number System CBSE Worksheets- 1 
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
∴ a = 11/7 and b = 6/7

Q.12. Evaluate: 
Class 9 Maths - Number System CBSE Worksheets- 1
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1 
Class 9 Maths - Number System CBSE Worksheets- 1

Q.13. Write the value of 
Class 9 Maths - Number System CBSE Worksheets- 1
Ans.
Class 9 Maths - Number System CBSE Worksheets- 1
Class 9 Maths - Number System CBSE Worksheets- 1
= 15

Q.14. Express Class 9 Maths - Number System CBSE Worksheets- 1 in p/q form.
Ans.
let x be the p/q form,
so, x = Class 9 Maths - Number System CBSE Worksheets- 1 
10x = Class 9 Maths - Number System CBSE Worksheets- 1
1000x = Class 9 Maths - Number System CBSE Worksheets- 1
1000x - 10x = Class 9 Maths - Number System CBSE Worksheets- 1-  Class 9 Maths - Number System CBSE Worksheets- 1
990x = 15555
x= 15555/990
= 1037/66

Q.15. Insert five rational no's between 3/5 and 4/5.
Ans.
3/5 and 4/5
Class 9 Maths - Number System CBSE Worksheets- 1
30/50 and 40/50
∴ pick any five number between 30 and 40
31/50,  32/50,  36/50,  37/50,  39/50


The document Class 9 Maths - Number System CBSE Worksheets- 1 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- 1

1. What is the definition of a number system in mathematics?
2. What are the different types of number systems taught in Grade 9?
Ans. In Grade 9, students typically learn about several types of number systems including natural numbers (1, 2, 3,...), whole numbers (0, 1, 2, 3,...), integers (...,-3, -2, -1, 0, 1, 2, 3,...), rational numbers (fractions like 1/2, -3/4), and irrational numbers (like √2, π). Each type has unique characteristics and applications.
3. How do you convert a fraction into a decimal?
Ans. To convert a fraction into a decimal, divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 into a decimal, you would calculate 3 ÷ 4, which equals 0.75.
4. What is the difference between rational and irrational numbers?
Ans. Rational numbers are numbers that can be expressed as a fraction of two integers (where the denominator is not zero), such as 1/2 or -3. In contrast, irrational numbers cannot be expressed as a simple fraction; they have non-repeating, non-terminating decimal expansions, such as √2 or π.
5. How can I determine if a number is rational or irrational?
Ans. To determine if a number is rational or irrational, check if it can be expressed as a fraction of two integers. If it can, it is rational. If it cannot be expressed this way, and its decimal form is non-repeating and non-terminating, then it is irrational. For example, 0.333... is rational (1/3), while π is irrational.
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