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RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9 PDF Download

RS Aggarwal Exercise 1.1 Number System

Q.1. Is zero a rational number? Justify.
Ans. Yes, 0 is a rational number.
0 can be expressed in the form of the fraction p/q,where p = 0 and q c an be any integer except 0.

Q.2. Represent each of the following rational number line:
(i) 5/7
(ii) 8/3
(iii)RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(iv) 1.3
(v) - 2.4
Ans.
(i) 5/7
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(ii) 8/3
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(iii)RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(iv) 1.3
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(v) – 2.4
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Q.3. Find a rational number between
(i) 3/8 and 2/5
(ii) 1.3 and 1.4
(iii) −1 and 1/2
(iv) RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9and RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(v) 1/9 and 2/9
Ans. (i) RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9and RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Let:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Rational number lying between x and y:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(ii) 1.3 and 1.4
Let:
x = 1.3 and y = 1.4
Rational number lying between x and y:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(iii) −1 and 1/2
Let:
x = -1 and y = 1/2
Rational number lying between x and y:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(iv) RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9 andRS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Let:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Rational number lying between x and y:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(v) 1/9 and 2/9
A rational number lying between 1/9 and 2/9 will be
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Q.4. Find three rational numbers lying between 3/5 and 7/8. How many rational numbers can be determined between these two numbers?
Ans.
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
n = 3
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Rational numbers between RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
(x + d),(x + 2d),...,(x + nd)
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9 
There are infinitely many rational numbers between two given rational numbers.

Q.5.

Find four rational numbers between 3/7 and 5/7.
Ans.
n = 4
n + 1 = 4 + 1 = 5
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Thus, rational numbers betweenRS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Q.6.
Find six rational numbers between 2 and 3.
Ans. x = 2, y = 3 and n = 6
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Thus, the required numbers are
(x + d),(x + 2d),(x + 3d),...,(x + nd)
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Q.7.
Find five rational numbers between RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Ans.
n = 5
n + 1 = 6
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
Thus, rational numbers between will RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9 be
(x + d),(x + 2d),(x + 3d),(x + 4d),(x + 5d)
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9

Q.8.
Insert 16 rational numbers between 2.1 and 2.2.
Ans.
Let:
x = 2.1, y = 2.2 and n = 16
We know:
RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9
So, 16 rational numbers between 2.1 and 2.2 are:
(x + d), (x + 2d), ...(x + 16d)
= [2.1 + 0.005], [2.1 + 2(0.005)],...[2.1 + 16(0.005)]
= 2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.155, 2.16, 2.165, 2.17,
2.175 and 2.18

Q.9. State whether the following statements are true or false. Give reasons for your answer.
(i) Every natural number is a whole number.
(ii) Every whole number is a natural number.
(iii) Every integer is a whole number.
(iv) Every integer is a rational number.
(v) Every rational number is an integer.
(vi) Every rational number is a whole number.
Ans. 
(i) Every natural number is a whole number.

True, since natural numbers are counting numbers i.e N = 1, 2,...
Whole numbers are natural numbers together with 0. i.e W = 0, 1, 2,...
So, every natural number is a whole number
(ii) Every whole number is a natural number.
False, as whole numbers contain natural numbers and 0 whereas natural numbers only contain the counting numbers except 0.
(iii) Every integer is a whole number.
False, whole numbers are natural numbers together with a zero whereas integers include negative numbers also.
(iv) Every integer is a rational number.
True, as rational numbers are of the form RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9where q ≠ 0. All integers can be represented in the form p/q where q ≠ 0.
(v) Every rational number is an integer.
False, as rational numbers are of the formRS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9where q ≠ 0. Integers are negative and positive numbers which are not in p/q form. For example, 1/2  is a rational number but not an integer.
(vi) Every rational number is a whole number.
False, as rational numbers are of the form p/q where q ≠ 0. Whole numbers are natural numbers together with a zero.
For example, 5/7 is a rational number but not a whole number. 

The document RS Aggarwal Solutions: Number System- 1 | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on RS Aggarwal Solutions: Number System- 1 - Mathematics (Maths) Class 9

1. What is the importance of learning the number system in mathematics?
Ans. The number system is the foundation of mathematics and is essential for various mathematical operations. It helps in understanding the concept of place value, performing arithmetic operations, and solving complex mathematical problems.
2. How can I improve my understanding of the number system?
Ans. To improve your understanding of the number system, you can practice solving numerical problems, work with different number representations such as fractions, decimals, and percentages, and learn various properties and rules associated with numbers. Additionally, seeking guidance from a teacher or using study materials like the RS Aggarwal book can also be helpful.
3. What are the different types of number systems?
Ans. There are various types of number systems, including the decimal number system, binary number system, octal number system, and hexadecimal number system. Each system has its own unique way of representing numbers and is used in different fields like computing, electronics, and mathematics.
4. How do I convert numbers from one number system to another?
Ans. To convert numbers from one number system to another, you can use specific conversion methods for each system. For example, to convert a decimal number to a binary number, you can use the division-by-2 method. Similarly, there are specific algorithms or formulas for converting between other number systems.
5. What are the applications of the number system in real life?
Ans. The number system has various applications in real life. It is used in finance and accounting for calculations, in computer programming and coding for data representation and manipulation, in engineering for measuring and analyzing data, and in everyday life for tasks like budgeting, shopping, and measuring quantities.
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