This is the Solution of exercise 1.1 from newly published book by PCTB (Punjab) for new 9th session 2025 Onward.
Exercise 1.1
Question # 01: Identify each of the following as rational or irrational number.
\((i)\) \(\quad 2.353535 \)
\((ii)\) \(\quad 0.\overline{6} \)
\((iii)\) \(\quad 2.236067… \)
\((iv)\) \(\quad \sqrt{7} \)
\((v)\) \(\quad e \)
\((vi)\) \( \quad \pi \)
\((vii)\) \(\quad 5+\sqrt{11} \)
\((viii)\) \(\quad\sqrt{3} +\sqrt{13} \)
\((ix)\) \(\quad\frac{15}{4} =3.75 \)
\((x)\) \(\quad\left( 2-\sqrt{2}\right)\left( 2+\sqrt{2}\right) \)
Question 2: Represent the following numbers on number line.
\((i)\) \(\quad \sqrt{2} \)
\((ii)\) \(\quad \sqrt{3} \)
\((iii)\) \(\quad 4\frac{1}{3} \)
\((iv)\) \(\quad -2\frac{1}{7} \)
\((v)\) \(\quad \frac{5}{8} \)
\((vi)\) \(\quad 2\frac{3}{4} \)
Question 3: Express the following as a rational number \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q\ne 0 \).
\((i)\) \(\quad 0.\overline{4} \)
\((ii)\) \(\quad 0.\overline{37} \)
\((iii)\) \(\quad 0.\overline{21} \)
Question 4: Name the property used in the following.
\((i)\) \(\quad \left(a+4\right)+b=a+\left(4+b\right) \)
\((ii)\) \(\quad \sqrt{2} +\sqrt{3} =\sqrt{3} +\sqrt{2} \)
\((iii)\) \(\quad x-x=0 \)
\((iv)\) \(\quad a\left(b+c\right)=ab+ac \)
\((v)\) \(\quad 16+0=16 \)
\((vi)\) \(\quad 100\times1=100 \)
\((vii)\) \(\quad 4\times \left(5 \times 8\right) = \left(4\times 5\right) \times 8 \)
\((viii)\) \(\quad ab=ba \)
Question 5: Name the property used in the following.
\((i)\) \(\quad -3< -1\ \Rightarrow \ 0< 2 \)
\((ii)\) \(\quad\) If \(a< b\) then \(\frac{1}{a} >\frac{1}{b}\)
\((iii)\) \(\quad\) If \(a<b\) then \(a+c< b+c\)
\((iv)\) \(\quad \) If \(ac<bc\) and \(c>0\) then \(a<b\)
\((v)\) \(\quad\) If \(ac<bc\) and \(c<0\) then \(a>b\)
\((vi)\) \(\quad\) Either \(a>b\) or \(a=b\) or \(a<b\)
Question 6: Insert two rational numbers between:
\((i)\) \(\quad\) \(\frac{1}{3}\) and \(\frac{1}{4}\)
\((ii)\) \(\quad\) \(3\) and \(4\)
\((iii)\) \(\quad\) \(\frac{3}{5}\) and \(\frac{4}{5}\)