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: Represent the following on a number line.
\((i)\) \(\quad x<0 \)
\((ii) \quad -3<x<3 \)
\((iii) \quad x\ge -8 \)
\((iv) \quad x>0 \)
\((v) \quad x<-3 \)
\((vi) \quad -4<x\le 4 \)
Question 4: Identify the properties of equality and inequality of real numbers that justifies the statement.
\((i)\) \(\quad 9x=9x \)
\((ii) \quad \text{If }x+2=y \)\(\text{ and }\)\(y=2x,\text{ then }x+2=2x-3 \)
\((iii) \quad \text{If 2}x+3=y,\text{ then }y=2x+3 \)
\((iv) \quad \text{If }3<4,\text{ then }-3>-4 \)
\((v) \quad \text{If }2y+2w=p\text{ and }p=50,\)\(\text{ then }\)\(2y+2w=50 \)
\((vi) \quad \text{If }x+4>y+4,\text{ then }x>y \)
\((vii) \quad \text{If }2<5\text{ and }5<9,\text{ then }2<9 \)
\((viii) \quad \text{If }-18<-16,\text{ then }9>8 \)