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Class 9 Maths Chapter 1 Question Answers - Number System

Q1: Simplify: (√5 + √2)2.
Ans:
Here, (√5 + √22 = (√52 + 2√5√2 + (√2)2
= 5 + 2√10 + 2
= 7 + 2√10

Q2:How many rational numbers can be found between two distinct rational numbers?
(i) Two
(ii) Ten
(iii) Zero
(iv) Infinite
Ans: (iv) Infinite
Between any two distinct rational numbers, an infinite number of rational numbers can be found. This is because rational numbers are dense on the number line, meaning between any two rational numbers aa and b (a < ba<b), you can always find another rational number by calculating the average:
New rational number = a+b/2 

Q3: Identify a rational number among the following numbers :
2 + √2, 2√2, 0 and π
Ans: 
0 is a rational number.


Q4:  √8 is an
(i) natural number
(ii) rational number
(iii) integer
(iv) irrational number

Ans: (D) 
\sqrt{8}
√8 is an irrational number
Therefore, √8 = √4 × 2 = 2√2


Q5: Find the value of √(3)- 2.
Ans:

√(3)−2 = (3−2)1/2 = 3−2 × 1/2 = 3−1 = 13

Q6:  Is zero a rational number? Can you write it in the form pq\frac{p}{q}, where pp and q are integers and q0q \neq 0?

Ans: Consider the definition of a rational number. A rational number is the one that can be written in the form pq\frac{p}{q} , where p and q are integers and q0q \neq 0

Zero can be written as

01,02,03,04,05,\frac{0}{1}, \frac{0}{2}, \frac{0}{3}, \frac{0}{4}, \frac{0}{5}, \dots

So, we arrive at the conclusion that 000 can be written in the form pq\frac{p}{q}, where pp is any integer.

Therefore, zero is a rational number.


Q7: A terminating decimal is

(i) a natural number
(ii) a rational number
(iii) a whole number
(iv) an integer.

Ans: (ii) a rational number

Q8: Find 64^{\frac{1}{2}}641/2
Ans:

64(1/2)
We know that a1/n = n√a, where a > 0.
We conclude that 64(1/2) can also be written as:
2√64 = 2√(8 × 8)
Therefore, the value of 64(1/2) will be 8.

Q9: Simplify Class 9 Maths Chapter 1 Question Answers - Number System
Ans:

Class 9 Maths Chapter 1 Question Answers - Number System

The LCM of 3 and 4 is 12.

21/3 = 24/12 = (24)1/12 = 161/12

31/4 = 33/12 = (33)1/12 = 271/12

Therefore, 21/3 × 31/4 = 161/12 × 271/12 = (16 × 27)1/12
= (432)1/12.

Q10: The sum of rational and an irrational number
(i) may be natural
(ii) may be irrational
(iii) is always irrational
(iv) is always rational

Ans: (iii) is always rational
Example: 
Rational number: 33
Irrational number: 2\sqrt{2
Sum: 3+2
The sum 3+23 + \sqrt{2} cannot be expressed as pq\frac{p}{q}, so it is irrational.

The document Class 9 Maths Chapter 1 Question Answers - Number System is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9
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FAQs on Class 9 Maths Chapter 1 Question Answers - Number System

1. What are the different types of number systems?
Ans. The main types of number systems include the decimal number system (base 10), binary number system (base 2), octal number system (base 8), and hexadecimal number system (base 16). Each system has its own set of digits and rules for representation.
2. How do you convert a binary number to decimal?
Ans. To convert a binary number to decimal, multiply each digit by 2 raised to the power of its position (starting from 0 on the right) and sum all the results. For example, the binary number 1011 converts to decimal as follows: (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0) = 8 + 0 + 2 + 1 = 11.
3. What is the importance of number systems in computer science?
Ans. Number systems are crucial in computer science because they form the basis for data representation and processing. Computers use the binary system for operations and data storage, while other systems like hexadecimal are used for more human-readable representations of binary data.
4. How do you convert a decimal number to binary?
Ans. To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainder. Continue dividing until the quotient is 0. The binary number is then formed by reading the remainders in reverse order. For example, to convert 13 to binary: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1, giving us 1101.
5. What is the difference between signed and unsigned numbers in binary?
Ans. Signed numbers in binary can represent both positive and negative values, typically using a method like two's complement. Unsigned numbers, on the other hand, can only represent non-negative values, effectively doubling the maximum value that can be represented compared to signed numbers of the same bit length.
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