Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Short Question Answers: Number System
Class 9 Maths Chapter 1 Question Answers - Number System
Q1. Find a rational number between 1 and 2.
Let x = 1 and y = 2, then
Thus, 3/2 is a rational number between 1 and 2.
Q2. Find two rational numbers between 0.1 and 0.3.
Let x = 0.1, y = 0.3 and n = 2
∴ Two rational numbers between 0.1 and 0.3 are: x + d and x + 2d
Q3. Express 
in the form of a decimal.
We have,
Now, dividing 25 by 8,
Since, the remainder is 0.
∴ The process of division terminates.
Q4. Express 
as a rational number.
Multiplying (1) by 100, we have 100x = 100 x 0.3333…
⇒ 100x = 33.3333 …(2)
Subtracting (2) from (1), we have
100x – x = 33.3333… – 0.3333…
⇒ 99x = 33
Q5. Simplify: (4+ √3) (4 −√3)
∵ (a + b)(a – b) = a2 – b2
(4 +√3) (4 −√3) = (4)2 – ( √3)2 = 16 – 3 = 13
Thus, (4 +√3) (4 −√3) = 13
Q6. Simplify: (√3 +√2)2
∵ (a + b)2 = a2 + 2ab + b2
(√3 +√2)2 = (√3)2 + √2 ( √3 ×2) + (√2)2 = 3 + 2 √6 + 2 = 5 + 2 √6
Thus, (√3 +√2)2 = 5 + 2√6
Q7. Rationalise the denominator of 
Since RF of (√x - √y ) is (√x +√y )
∴ RF of (√3 - √2 ) is (√3 +√2 )
Now, we have
Thus,
Q8. Find 
As, 64 = 4 x 4 x 4 = 43
Q9. Find a rational number lying between 
Rational numbers between 1/2 and 1/5 are infinite. Some of them are 3/10 , 4/10 , 45/100 , 35/100. Step-by-step explanation: As per the question, We need to find drational numbers lying between 1/5 and 1/2 As we know,Hence, Rational numbers between 1/2 and 1/5 are infinite. Some of them are 3/10 , 4/10 , 45/100 , 35/100.
- Rational Numbers are numbers that can be expressed in the form of p/q where q is not equal to zero.
- Now, we know that 1/5 = 0.2 and 1/2 = 0.5
- So, numbers between 0.2 and 0.5 are infinite. Some of them are 0.3,0.4,0.45,,0.35 etc.
- And these may be written as 3/10,4/10,45/100,35/100 tec.
Q10. Express 
as a fraction in the simplest form.
Let X =
Then, multiplying (1) by 10,
We have 10X = 10 x 0.24545...
⇒ 10x = 2.4545 ... (2)
Again multiplying (1) by 1000,
we get 1000 x X = 0.24545... x 1000
⇒ 1000X = 245.4545 ... (3)
Subtracting (2) from (3),
1000X – 10X = 245.4545... – 2.4545...
Thus
The document Class 9 Maths Chapter 1 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 Chapter 1 Question Answers - Number System
| 1. What is the decimal number system? |  |
Ans. The decimal number system is a base-10 number system that uses the digits 0-9 to represent numbers. Each digit's position in a number determines its value, with the rightmost digit representing ones, the next representing tens, and so on.
| 2. How does the binary number system work? | |
Ans. The binary number system is a base-2 number system that uses only the digits 0 and 1 to represent numbers. Each digit's position in a binary number represents a power of 2, with the rightmost digit representing 2^0, the next representing 2^1, and so on.
| 3. What is the hexadecimal number system? | |
Ans. The hexadecimal number system is a base-16 number system that uses the digits 0-9 and the letters A-F to represent numbers. Each digit in a hexadecimal number represents a power of 16, with the rightmost digit representing 16^0, the next representing 16^1, and so on.
| 4. How can numbers be converted between different number systems? | |
Ans. Numbers can be converted between different number systems by using the concept of place value. To convert a number from one system to another, you can convert it to its decimal equivalent first and then convert it to the desired number system.
| 5. Why are different number systems used in computing? | |
Ans. Different number systems, such as binary and hexadecimal, are used in computing because they align well with the way computers process data. Binary is the fundamental number system in computing because computers use switches that can be in two states (on/off), making it easy to represent data using 0s and 1s. Hexadecimal is used as a shorthand for binary in programming and allows for more compact representation of data.
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