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.

Sol: Express 1 and 2 as rational numbers with the same denominator:
1 = 1010, 2 = 2010
Now, the rational numbers between 1010 and 2010 are:
1110, 1210, 1310, 1410, 1510, 1610, 1710, 1810, 1910
Out of these, select any five:

1110, 1210, 1310, 1410, 1510
Answer:
The five rational numbers between 1 and 2 are:
1110, 1210, 1310, 1410, 1510\frac{11}{10}, \frac{12}{10}, \frac{13}{10}, \frac{14}{10}, \frac{15}{10}


Q2. Find two rational numbers between 0.1 and 0.3.

Sol:  Express 0.10.1 and 0.30.3 as rational numbers with the same denominator:

0.1=1100.3=310

Now, the rational numbers between 110\frac{1}{10} and 310\frac{3}{10} can be written with a larger denominator to find numbers in between.
Let us express them with a denominator of 100100100:

0.1=10100 ,0.3=30100  .

The rational numbers between 10100\frac{10}{100} and 30100\frac{30}{100} are:

11100,12100,13100,,29100.\frac{11}{100}, \frac{12}{100}, \frac{13}{100}, \ldots, \frac{29}{100}

any two:

12100,25100.\frac{12}{100}, \frac{25}{100}.


Q3. Express  3 18 in the form of a decimal.

We have, 3 18 = 258
Now, dividing 25 by 8,
Class 9 Maths Chapter 1 Question Answers - Number System 

Since, the remainder is 0.
∴ The process of division terminates.

258 = 3.125

Thus, 3 18 = 3.125


Q4. Express  0.33  as a rational number.

Let x = 0.33 = 0.3333... (1)
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

x = 3399 = 13

Thus, 0.33 = 13

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 = a+ 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  1√6 - √5

Multiply and divide the given number by √6 + √5

 1√6 - √5

= √6 + √5(√6 - √5) (√6 + √5)

= √6 + √56 - 5

= √6 + √5

Q8. Find (64)-1/3

As, 64 = 4 x 4 x 4 = 43

∴ (64)-1/3 = 1(64)1/3 = 1(43)1/3
= 143×1/3 = 14
Thus, (64)-1/3 = 14


Q9. Find a rational number lying between 15  and  12

Rational numbers between   12 and  15 are infinite. Some of them are  310 ,   410 ,   45100 ,  35100  .Step-by-step explanation:As per the question, We need to find drational numbers lying between   15  and  12  As we know,
  • 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  15 = 0.2 and 12  = 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  310 ,   410 ,   45100 ,  35100  etc.
Hence, Rational numbers between 15  and  1are infinite. Some of them are 310 ,   410 ,   45100 ,  35100


Q10. Express  0.245  as a fraction in the simplest form.

Let X =0.245 = 0.24545 ... (1)
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...

⇒ 990x = 243

⇒ x24390027110

Thus, 0.24527110

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 are the different types of number systems?
Ans. The different types of number systems include the decimal system (base 10), binary system (base 2), octal system (base 8), and hexadecimal system (base 16). Each system has its own base and is used in various applications, such as computing and digital electronics.
2. How do you convert a binary number to a decimal number?
Ans. To convert a binary number to a decimal number, you multiply each bit by 2 raised to the power of its position (starting from 0 on the right) and then sum the results. For example, the binary number 1011 is calculated as (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0) = 8 + 0 + 2 + 1 = 11 in decimal.
3. What is the significance of the hexadecimal number system in computing?
Ans. The hexadecimal number system is significant in computing because it provides a more human-friendly representation of binary-coded values. It is commonly used in programming, memory addressing, and digital electronics since one hexadecimal digit represents four binary digits (bits), making it easier to read and write large binary numbers.
4. Can you explain how to perform addition in the binary number system?
Ans. To perform addition in the binary number system, you follow similar rules as decimal addition, but with only two digits (0 and 1). If you add 0 + 0, the result is 0; 0 + 1 and 1 + 0 both equal 1; and 1 + 1 equals 10 in binary (which is 2 in decimal, so you carry over 1 to the next column).
5. What are the applications of the octal number system?
Ans. The octal number system is primarily used in computing and digital electronics, particularly in older computing systems and Unix file permissions. It simplifies binary representation by grouping bits into sets of three, making it more manageable for certain programming tasks and electronic circuit design.
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