Chapter 1 : Number System

In Chapter 1 of Mathematics Class 9, we cover number comparison, notation systems, and number evaluations. All questions are crucial from an exam perspective.

  • Press the button at the bottom of the last question to know your total score.
  • No negative marking.

2868

1. The value of $1.999 \ldots$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$, is

2863

2. The product of any two irrational numbers is

2869

3. $2 \sqrt{3}+\sqrt{3}$ is equal to

2860

4. Every rational number is

2877

5. The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals

2864

6. The decimal expansion of the number $\sqrt{2}$ is

2870

7. $\sqrt{10} \times \sqrt{15}$ is equal to

2875

8. If $\sqrt{2}=1.4142$, then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to

2867

9. A rational number between $\sqrt{2}$ and $\sqrt{3}$ is

2872

10. $\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

2873

11. After rationalising the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}}$, we get the denominator as

2861

12. Between two rational numbers

2865

13. Which of the following is irrational?

2874

14. The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equal to

2880

15. Which of the following is equal to $x$ ?

Important Definitions and Rules

Rational Number:
A number is called a rational number if it can be expressed in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Irrational Number:
A number that cannot be written in the form of $\frac{p}{q}$ (where $p$ and $q$ are integers and $q \neq 0$) is called an irrational number.

Real Numbers:
The collection of all rational and irrational numbers is called real numbers.

Decimal Expansion of Real Numbers:
The decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating and non-recurring.

Note: If $r$ is a rational number and $s$ is an irrational number then-
1. $r+s$ and $r-s$ are irrational numbers.
2. Additionally, if $r$ is a non-zero rational number then $rs$ and $\frac{r}{s}$ are irrational numbers.


For positive real numbers $a$ and $b$:
(i) $\sqrt{ab}=\sqrt{a}\sqrt{b}$
(ii) $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
(iii) $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})=a-b$
(iv) $(a+\sqrt{b})(a-\sqrt{b})=a^2-b$
(v) $(\sqrt{a}+\sqrt{b})^2=a+2\sqrt{ab}+b$

If $p$ and $q$ are rational numbers and $a$ is a positive real number, then-
(i) $a^pa^q=a^{p+q}$
(ii) ${\left(a^p\right)}^q=a^{pq}$
(iii) $\frac{a^p}{a^q}=a^{p-q}$
(iv) $a^pb^p=(ab)^p$

Conclusion

Chapter 1: Number System in Class 9 Mathematics strengthens students' foundational knowledge in math. It includes all basic concepts and important questions useful for exams.