The NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 provide clear, accurate solutions to these problems in a way that makes the concepts easier to understand. The solutions here are curated by subject experts at Allen, according to the latest CBSE Syllabus, and also explain textbook problems clearly while strengthening your logical thinking and problem-solving skills.
The Number System forms an essential basis for mathematical skills and knowledge. The Class 9 Maths Chapter 1 acts as a foundation for many topics you will cover in later classes.
Exercise 1.1 of the NCERT Solutions for Class 9 Maths Chapter 1 contains questions that help students understand essential concepts such as
1. Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q≠0?
Sol. Yes, zero is a rational number. We can write zero in the form p/q where p and q are integers and q≠0.
So, 0 can be written as 0/1 = 0/2 = 0/3 etc.
2. Find six rational numbers between 3 and 4.
Sol. First rational number between 3 and 4 is (3+4)/2 = 7/2.
Similarly, other numbers are:
(3+7/2)/2 = (13/2)/2 = 13/4
(3+13/4)/2 = (25/4)/2 = 25/8
(3+25/8)/2 = (49/8)/2 = 49/16
(3+49/16)/2 = (97/16)/2 = 97/32
(97/32+3)/2 = (193/32)/2 = 193/64
So, numbers are 7/2, 13/4, 25/8, 49/16, 97/32, 193/64.
3. Find five rational numbers between 3/5 and 4/5.
Sol. To find rational numbers between 3/5 and 4/5, we can multiply the numerator and denominator by (n+1), where n is the number of rational numbers we want to find (here, n=5). So, n+1=6.
(3/5) × (6/6) = 18/30
(4/5) × (6/6) = 24/30
So, required rational numbers are 19/30, 20/30, 21/30, 22/30, 23/30.
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.
Sol. (i) True, the collection of whole numbers contains all natural numbers (Whole numbers = {0, 1, 2, 3, ...}, Natural numbers = {1, 2, 3, ...}).
(ii) False, -2 is an integer but it is not a whole number. (Integers = {..., -2, -1, 0, 1, 2, ...})
(iii) False, 1/2 is a rational number but not a whole number. (Rational numbers include fractions).
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