Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Additional Question Answers: Number System

Class 9 Maths Question Answers - Number System

Class 9 Maths Question Answers - Number System

Q1. Write four rational numbers equivalent to 5/7.

We have,
Class 9 Maths Question Answers - Number System
Four rational numbers equivalent to 5/7 are 10/14, 15/21, 20/28, 25/35.


Q2. Find nine rational numbers between 0.1 and 0.2.

Let x = 0.1, y = 0.2 and n = 9.
Class 9 Maths Question Answers - Number SystemThe nine rational numbers between x and y are:
(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d), (x + 6d), (x + 7d), (x + 8d) and (x + 9d).
Nine rational numbers between 0.1 and 0.2 are:
(0.1 + 0.01); (0.1 + 0.02); (0.1 + 0.03); (0.1 + 0.04); (0.1 + 0.05); (0.1 + 0.06); (0.1 + 0.07); (0.1 + 0.08) and (0.1 + 0.09)
The nine rational numbers between 0.1 and 0.2 are 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 and 0.19.


Q3. ExpressClass 9 Maths Question Answers - Number System as a rational number in simplest form.

Class 9 Maths Question Answers - Number System
⇒ 100x = 100 x (0.3838…)
⇒ 100x = 38.3838...(2)
Subtracting (1) from (2),
We have, 100x – x = (38.3838…) – (0.3838…)
Class 9 Maths Question Answers - Number System


Q4. Express Class 9 Maths Question Answers - Number System in the form of Class 9 Maths Question Answers - Number System.

Class 9 Maths Question Answers - Number System
∴ 10x = 10 x (0.5353…)
or 10x = 5.333... ...(1)
Also, 100x = 53.333... ...(2)
Subtracting (1) from (2),
⇒ 100x – 10x = (53.333…) – (5.333…)
⇒ 90x = 48

Class 9 Maths Question Answers - Number System

Class 9 Maths Question Answers - Number System


Q5. Express Class 9 Maths Question Answers - Number System is the form of p/q in the simplest form.

Class 9 Maths Question Answers - Number System
∴ 1000x = 1000 x (0.003003…)
or 1000x = 3.003003... …(2)
Subtracting (1) from (2),
We have 1000x – x = (3.003003…) – (0.003003…)
⇒ 999x = 3
⇒ x = 3/999 = 1/333
Thus,Class 9 Maths Question Answers - Number System


Q6. Find the sum of  (3√3 +7√2) and (√3 - 5√2)

We have  (3√3 +7√2) + (√3 - 5√2)
⇒ √3 3+7√2 + √3 - 5√2
⇒ (3√3+√3) + 7√2 - 5√2)
⇒ √3(3+1) + √2(7-2)
⇒ √3(4) + √2(5) = (4√3 + 2√2)


Q7. Divide 15 √12 by 3√3.

Class 9 Maths Question Answers - Number System


Q8. Rationalize the denominator ofClass 9 Maths Question Answers - Number System

Class 9 Maths Question Answers - Number System 
Class 9 Maths Question Answers - Number System (Prime factorize the numbers under the root in the denominator)
Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System

Q9. Rationalize the denominator of Class 9 Maths Question Answers - Number System

Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System


Q10. If ‘a’ and ‘b’ are rational numbers and Class 9 Maths Question Answers - Number System find the values of ‘a’ and ‘b’.

Class 9 Maths Question Answers - Number System              Class 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System

Comparing Class 9 Maths Question Answers - Number System


Q11. If Class 9 Maths Question Answers - Number System, what is the value of x3 - 5x2 + 8x - 4? 

Class 9 Maths Question Answers - Number System
(x - 2)3 = x3 - 6x2 + 12x - 8 ...(1)
(x - 2)2 = x2 - 4x + 4 ... (2) 
(1) + (2) = x3 - 5x2 + 8x - 4 

Class 9 Maths Question Answers - Number System


Q12. Find the value of Class 9 Maths Question Answers - Number System when Class 9 Maths Question Answers - Number System

Class 9 Maths Question Answers - Number System
∵   Class 9 Maths Question Answers - Number SystemClass 9 Maths Question Answers - Number SystemClass 9 Maths Question Answers - Number System
Class 9 Maths Question Answers - Number System

Q13. Rationalise the denominator of 1/[7+3√3].

1/(7 + 3√3)

By rationalizing the denominator,

= [1/(7 + 3√3)] [(7 – 3√3)/(7 – 3√3)]

= (7 – 3√3)/[(7)2 – (3√3)2]

= (7 – 3√3)/(49 – 27)

= (7 – 3√3)/22

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

1. What are the different types of number systems?
Ans. Number systems include decimal (base-10), binary (base-2), octal (base-8), and hexadecimal (base-16) systems.
2. How do you convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, divide the decimal number by 2 and note the remainders. The binary number is the sequence of remainders read from bottom to top.
3. What is the significance of the base in number systems?
Ans. The base of a number system determines the number of different digits used in that system and the value associated with each position in a number.
4. How do you convert a binary number to a decimal number?
Ans. To convert a binary number to a decimal number, multiply each digit by 2 raised to the power of its position from right to left, then add the results.
5. Why is the hexadecimal system commonly used in computer programming?
Ans. The hexadecimal system is used in computer programming because it can represent large binary numbers more compactly than binary or decimal systems, making it easier for programmers to work with memory addresses and binary data.
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