Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Short & Long Question Answer: Number Systems

Class 9 Maths Question Answers - Number System

Q1: Find five rational numbers between 1 and 2.
Sol:
We have to find five rational numbers between 1 and 2.
So, let us write the numbers with denominator 5 + 1 = 6
Thus, 6/6 = 1, 12/6 = 2
From this, we can write the five rational numbers between 6/6 and 12/6 as:
7/6, 8/6, 9/6, 10/6, 11/6

Q2: Locate √3 on the number line.
Sol:
Class 9 Maths Question Answers - Number SystemConstruct BD of unit length perpendicular to OB (here, OA = AB = 1 unit) as shown in the figure.
By Pythagoras theorem,
OD = √(2 + 1) = √3
Taking O as the centre and OD as radius, draw an arc which intersects the number line at the point Q using a compass.
Therefore, Q corresponds to the value of √3 on the number line.

Q3: Find the decimal expansions of 10/3, 7/8 and 1/7.
Sol:
Class 9 Maths Question Answers - Number SystemTherefore, 10/3 = 3.3333…
7/8 = 0.875
1/7 = 0.1428571…

Q4: What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
Sol:
Class 9 Maths Question Answers - Number SystemThus, 1/17 = 0.0588235294117647….
Therefore, 1/17 has 16 digits in the repeating block of digits in the decimal expansion.

Q5: Visualise 3.765 on the number line, using successive magnification.
Sol:
Visualisation of 3.765 on the number line, using successive magnification is given below:
Class 9 Maths Question Answers - Number System
Q6: Simplify: (√3+√7) (√3-√7).
Sol:
(√3 + √7)(√3 – √7)
Using the identity (a + b)(a – b) = a2 – b2,
(√3 + √7)(√3 – √7) = (√3)2 – (√7)2
= 3 – 7
= -4

Q7: Find five rational numbers between 3/5 and 4/5.
Sol:
We have to find five rational numbers between 3/5 and 4/5.
So, let us write the given numbers by multiplying with 6/6, (here 6 = 5 + 1)
Now,
3/5 = (3/5) × (6/6) = 18/30
4/5 = (4/5) × (6/6) = 24/30
Thus, the required five rational numbers will be: 19/30, 20/30, 21/30, 22/30, 23/30

Q8: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
Sol:
No, since the square root of a positive integer 16 is equal to 4. Here, 4 is a rational number.

Q9: Find three different irrational numbers between the rational numbers 5/7 and 9/11.
Sol:
The given two rational numbers are 5/7 and 9/11.
5/7 = 0.714285714…..
9/11 = 0.81818181……
Hence, the three irrational numbers between 5/7 and 9/11 can be:
0.720720072000…
0.730730073000…
0.808008000…

Q10: Add 2√2+ 5√3 and √2 – 3√3.
Sol:
(2√2 + 5√3) + (√2 – 3√3)
= 2√2 + 5√3 + √2 – 3√3
= (2 + 1)√2 + (5 – 3)√3
= 3√2 + 2√3

The document Class 9 Maths 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 Question Answers - Number System

1. What are the different types of number systems used in mathematics?
Ans. The main types of number systems include the Natural Number System (N), which consists of all positive integers starting from 1; the Whole Number System (W), which includes all natural numbers and zero; the Integer Number System (Z), which encompasses all positive and negative whole numbers; the Rational Number System (Q), containing all numbers that can be expressed as a fraction of integers; the Irrational Number System, which includes numbers that cannot be expressed as a simple fraction; and the Real Number System (R), which combines both rational and irrational numbers. Finally, the Complex Number System (C) includes all numbers in the form of a + bi, where a and b are real numbers and i is the imaginary unit.
2. How do you convert a binary number to a decimal number?
Ans. To convert a binary number to a decimal number, you need to multiply each digit of the binary number by 2 raised to the power of its position, counting from right to left and starting at 0. For example, to convert the binary number 1011 to decimal, you calculate: (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, which uses base 16, is significant in computing because it provides a more human-friendly representation of binary-coded values. Each hexadecimal digit represents four binary digits (nibbles), making it easier to read large binary values. It is commonly used in programming and web design, especially in color coding (e.g., #FFFFFF for white) and memory addresses.
4. What are rational and irrational numbers, and how do they differ?
Ans. Rational numbers are numbers that can be expressed as a fraction of two integers (where the denominator is not zero), such as 1/2, -3, or 4.75. Irrational numbers, on the other hand, cannot be expressed as a fraction; they have non-repeating, non-terminating decimal expansions, such as π (pi) or √2. The key difference lies in their representation: rational numbers can be written as fractions, while irrational numbers cannot.
5. How are number systems relevant in real-world applications?
Ans. Number systems are crucial in various real-world applications, including computer science, engineering, and finance. In computing, different number systems (like binary, octal, and hexadecimal) are used for data representation and processing. In engineering, number systems help in circuit design and analysis. In finance, they are used for calculations involving interest rates, investments, and data modeling. Understanding these systems is essential for problem-solving and analytical skills in numerous fields.
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