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

Number System Class 9 Worksheet Maths Chapter 1

Q.1. The value of Number System Class 9 Worksheet Maths Chapter 1 is
(a) 0.45
(b) Number System Class 9 Worksheet Maths Chapter 1
(c) 45/1000
(d) Number System Class 9 Worksheet Maths Chapter 1
Ans.

Number System Class 9 Worksheet Maths Chapter 1
9900 x = 2300
x = 23/99
Similarly x = 22/99
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1

Q.2. If n is a natural number, then √n is
(a) 
Always a natural number
(b) 
Always a rational number
(c) 
Always a irrational number
(d) 
Sometimes a natural number and sometimes a surd
Ans. 
(d)

Q.3. If  

Number System Class 9 Worksheet Maths Chapter 1 
prove m-n = 1
Ans. 

Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
⇒ 33n - 3m +3 = 30
⇒ 3n - 3m +3 = 0
⇒ n - m +1 = 0
⇒ m- n = 1

Q.4. The value of  ((23 + 22)2/3 + (150 - 29)1/2)2 is
(a) 
196
(b) 
286
(c) 
400
(d) 
324
Ans. 
(c)
((23 + 22)2/3 + (150 - 29)1/2)2
((23 + 4)2/3 + (121)1/2)2
((27)2/3 + (121)1/2)2
((33)2/3 + (11))2
(9+11)2  = 20 = 400
Hence option (c) is correct.

Q.5. If 
Number System Class 9 Worksheet Maths Chapter 1 

find a2 - b, a+ b
Ans.
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
= -9 - 4√5
a+b = 4√5 - 9 - 9 - 4√5 = -18
a-b = 4√5 - 9 + 9  + 4√5 = 8√5
a- b2 = (a+b)(a-b)
= -18 x 8√5
= - 144√5

Q.6. Give any two rational number between the irrational numbers 0.515115111511115....  and 0.53533533353333.... 
Ans. 
Pick any two number between them;
0.521, 0.527

Q.7. Explain the difference between rational number and irrational number with example.
Ans.
Rational number are those numbers expressed in the form of p/q, where p and q are co-primes & q ≠0.
Example: √2, √3, √11 etc.
Irrational numbers can't be expressed in the form mentioned above.
Example: 2, 3/4, 4/3, 0, 1, -2

Rational and Irrational numbersRational and Irrational numbers

Q.8. Find a if 
Number System Class 9 Worksheet Maths Chapter 1
Ans.
Number System Class 9 Worksheet Maths Chapter 1 
Squaring both side,
13 - a√10 = 8+5+ 2√40
-a√10  = 2√40
Number System Class 9 Worksheet Maths Chapter 1
a = -4

Q.9. If x + √13 = 4, find the value of x -1/x
Ans.
Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1


Q.10. Find the value of 
Number System Class 9 Worksheet Maths Chapter 1
Ans.
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1

Q.11. Simplify (11+√11)(11-√11)
Ans. 
112 - 11 = 121 -11 = 110

Q.12. Find x and y if 
Number System Class 9 Worksheet Maths Chapter 1
Ans.
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
x = 13, y = -3

Q.13. find the value of  
Number System Class 9 Worksheet Maths Chapter 1
Ans. 
Number System Class 9 Worksheet Maths Chapter 1

Q.14. Simplify Number System Class 9 Worksheet Maths Chapter 1 
if x = √7 + √6
Ans. 
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
= 13 + 2√42 + 13 - 2√42 - 2
= 24

Q.15. If xy = 1 and x = 7 + 4√3, what is the value of  
Number System Class 9 Worksheet Maths Chapter 1
Ans. 
x = 7 + 4√3
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
Number System Class 9 Worksheet Maths Chapter 1
1/x = y and y = 1/x,
so,
Number System Class 9 Worksheet Maths Chapter 1
= (7 - 4√3)2 + (7 + 4√3)2 
= 49-48 - 56√3 + 49 + 48 + 56√3
= 194

Q.16. Find x  if 4x - 4x-1 = 24.
Ans.
Number System Class 9 Worksheet Maths Chapter 1
suppose 4x = m
m - m/4 = 24
3m/4 = 24
m = (24 x 4)/3
m = 32
∴ 4x = 32
= 22x = 25
= 2x = 5
= x = 5/2

Q. 17. if x = 2 and y = 4, what is value of (x/y)x-y + (y/x)y-x
Ans. (2/4)-2 + (4/2)4-2 = 22 + 22 = 8

Q.18. Simplify 
Number System Class 9 Worksheet Maths Chapter 1
Ans.
 Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

Number System Class 9 Worksheet Maths Chapter 1

The document Number System Class 9 Worksheet Maths Chapter 1 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Number System Class 9 Worksheet Maths Chapter 1

1. What are the different types of numbers in the number system?
Ans. The different types of numbers in the number system include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
2. How do you classify numbers as even or odd?
Ans. Numbers are classified as even if they are divisible by 2 without leaving a remainder, and odd if they are not divisible by 2 without leaving a remainder.
3. Can you explain the concept of prime numbers?
Ans. Prime numbers are numbers greater than 1 that have only two factors, 1 and the number itself. They cannot be divided evenly by any other number.
4. How do you convert a decimal number to a fraction?
Ans. To convert a decimal number to a fraction, the decimal number is written as a fraction with the decimal part as the numerator and a power of 10 as the denominator. The fraction is then simplified if possible.
5. What is the significance of the number zero in the number system?
Ans. Zero is a unique number in the number system as it acts as a placeholder, indicating the absence of a quantity. It also serves as the additive identity, meaning any number added to zero remains unchanged.
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