Class 9 Math Ch 1 Number Systems Ex 1.1, builds on the number concepts learned in earlier classes and introduces new types of numbers like irrational numbers. Exercise 1.1 focuses mainly on understanding the representation of irrational numbers on the number line and helps students distinguish between rational and irrational numbers. This exercise lays the groundwork for mastering the real number system, which includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers. By practicing Exercise 1.1, students develop a clear understanding of how different types of numbers fit together within the number system
Class 9 Math Ch 1 Number Systems Ex 1.1 – Textbook
Question 1.
Is zero a rational number? Can you write it in the form p/q ,where p and q are integers and q ≠0?
Solution: Yes, zero is a rational number.
A rational number is any number that can be expressed in the form: p/q where p and q are integers, and q≠0
Zero can be written as: 0/1
Here:
- p=0 (an integer),
- q=1 (an integer), and
- q≠0
Thus, zero fits the definition of a rational number because it can be written as a fraction where the numerator is an integer and the denominator is a non-zero integer.
Ex 1.1 Class 9 Maths Question 2.
Find six rational numbers between 3 and 4.
Solution:
We need to find six rational numbers that lie between 3 and 4.
Let’s express 3 and 4 with the same denominator:
3 = 30/10
4 = 40/10
Now, choose six rational numbers between 30/10 and 40/10:
31/10, 32/10, 33/10, 34/10, 35/10, 36/10
These are:
3.1, 3.2, 3.3, 3.4, 3.5, 3.6
Question 3.
Find five rational numbers between 3/5 and 4/5.
Solution:
To find five rational numbers between 3/5 and 4/5, we first convert them to equivalent fractions with a larger common denominator.
Multiply both numerator and denominator of 3/5 and 4/5 by 10:
3/5 = 30/50
4/5 = 40/50
Now, pick five rational numbers between 30/50 and 40/50:
31/50, 32/50, 33/50, 34/50, 35/50
Question 4.
State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
Solution:
(i) Every natural number is a whole number.
Answer: True
Reason: Natural numbers are counting numbers starting from 1 (1, 2, 3, …), and whole numbers start from 0 (0, 1, 2, 3, …). So, every natural number is also a whole number.
(ii) Every integer is a whole number.
Answer: False
Reason: Integers include both negative and positive numbers (…, -3, -2, -1, 0, 1, 2, 3, …), but whole numbers are only non-negative numbers (0, 1, 2, 3, …). So, negative integers are not whole numbers.
(iii) Every rational number is a whole number.
Answer: False
Reason: Rational numbers include fractions and decimals (like 1/2, 3/4, 5.6), which are not whole numbers. Only rational numbers that are non-negative integers (like 0, 1, 2, etc.) are whole numbers.
Class 9 Math Ch 1 Number Systems Ex 1.1 is important for building a strong foundation in mathematics because it introduces students to the concept of irrational numbers and their placement on the number line. This forms the basis for understanding the entire real number system, which is a key component in higher-level math topics. Through this exercise, students learn how to identify irrational numbers and represent them accurately using the number line, which enhances their visual understanding of abstract concepts.
Moreover, Class 9 Math Ch 1 Number Systems Ex 1.1 of Number Systems is important for building a strong foundation in mathematics as it helps students differentiate between rational and irrational numbers, reinforcing their previous knowledge and connecting it to new concepts. These fundamental skills are not only useful in exams but also in solving real-life problems that involve data, measurement, and estimation.
The repeated practice of such questions ensures clarity and confidence, especially when moving on to advanced algebraic operations. Class 9 Math Ch 1 Number Systems Ex 1.1 of Number Systems is important for building a strong foundation in mathematics, and mastering it ensures that students are well-prepared for all upcoming chapters.
To conclude, Exercise 1.1 of Number Systems is important for building a strong foundation in mathematics and must be practiced thoroughly for long-term success.
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