Detailed solution to all exercise questions of NCERT book for CBSE Class 9 Math in Chapter 1 - Number Systems - exercise 1.1. The exercise comprises 4 questions.
Key concepts covered in this exercise include properties of rational numbers, natural numbers, whole numbers, and integers. Finding rational numbers between two numbers. Expressing rational numbers in the form \\frac{p}{q}), where p and q are integers and q is not zero.
Is 0 a rational number? Can you write it in the form \\frac{p}{q}), where p and q are integers and q ≠ 0?
Zero is a rational number.
Zero can be written in the form \\frac{p}{q}), where p and q are integers and q ≠ 0 as \\frac{0}{1})
Find six rational numbers between 3 and 4.
Step 1: To obtain six rational numbers between 3 and 4, we must multiply and divide both 3 and 4 by 7.
Why 7?
By multiplying and dividing by 7, we are increasing the gap between 3 and 4 by 7 times. So, 6 numbers can be fitted between them.
So, the rule is always to multiply and divide it by a number that is 1 more than the number of numbers to be fitted between the given numbers.
3 will consequently become \\frac{21}{7}) and 4 will become \\frac{28}{7})
Essentially, now we have to find 6 numbers between \\frac{21}{7}) and \\frac{28}{7})
Notice that between 21 and 28 we can fit 6 integers.
Step 2: Write integers from 22 to 27 and divide them by 7 to get the 6 numbers between 3 and 4.
The numbers are therefore, \\frac{22}{7}), \\frac{23}{7}), \\frac{24}{7}), \\frac{25}{7}), \\frac{26}{7}), and \\frac{27}{7}).
Find five rational numbers between \\frac{3}{5}) and \\frac{4}{5}).
Step 1: To obtain five rational numbers between \\frac{3}{5}) and \\frac{4}{5}), we must multiply and divide both \\frac{3}{5}) and \\frac{4}{5}) by 6.
Why 6?
By multiplying and dividing by 6, we are increasing the gap between \\frac{3}{5}) and \\frac{4}{5}) 6 times. So, 5 numbers can be fitted between them.
\\frac{3}{5}) will consequently become \\frac{18}{30}) and \\frac{4}{5}) will become \\frac{24}{30})
Essentially, now we have to find 6 numbers between \\frac{18}{30}) and \\frac{24}{30})
Notice that between 18 and 24 we have 5 integers.
Step 2: Write integers from 19 to 23 and divide them by 30 to get the 5 numbers between \\frac{3}{5}) and \\frac{4}{5}).
The numbers are therefore, \\frac{19}{30}), \\frac{20}{30}), \\frac{21}{30}), \\frac{22}{30}), and \\frac{23}{30}).
State whether the following statements are true or false with reasons.
i): Every natural number is a whole number.
TRUE. Whole numbers include 0 as well as all the natural numbers. So, every natural number is a whole number.
ii): Every integer is a whole number.
FALSE. Negative integers are not whole numbers.
However, note that all whole numbers are integers.
iii): Every rational number is a whole number.
FALSE. Whole numbers are non-negative numbers.
Negative rational numbers and rational numbers whose denominators ≠ 1 are not whole numbers.
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