- Natural and Whole Number
- |
- Integers
- |
- Rational and Irrational Numbers
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- Real Numbers
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- Laws of exponents
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- What is Number Line
- |
- successive Magnification

Here we are trying to give the Class 9 Maths Important Questions for Number System. It tests the basic concepts and at the same makes the student comfortable with the questions

1. Without actually performing division, state which of these number will terminating decimal expression or non terminating repeating decimal expression

- 7/25
- 3/7
- 29/343
- 6/15
- 77/210
- 11/67
- 15/27

Solution

Those rational number which can be expressed in form x/2^{m} X5^{n} are terminating expression and those can not be are non terminating decimal expression

Terminating decimal: (a), (d)

Non terminating repeating decimal: (b), (c), (e), (f), (g)

2. Rationalize the expression

a) $\frac{2+\sqrt{3}}{2-\sqrt{3}}$

b)$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

Solution

3) Write 10 rational number between

a) 4 and 5

b) 1/2 and 1/3

4) Represent in rational form.

a)1.232323….

b) 1.25

c) 3.67777777

5) Prove that $2+\sqrt{3}$ is a irrational number

6) **True or False statement**

a) Every Real number is a Rational numbers

b) Every irrational number is a Real numbers

c) Every whole number is a natural number

d) Every integer is a rational number

e) Every rational number is a whole number

f) There are infinite integers between two integers

g) There are finite rational number between 2 and 3

h) $\sqrt{3}$ Can be expressed in the form $\sqrt{3}$/1,so it is a rational number

Solution

- False ,since real number includes both rational and irrational number
- True
- False,as 0 is not natural number
- True ,as any integer can be expressed in the form p/q
- False
- False,There are finite integer between two integers
- False
- False

__Multiple choice Questions__

7) which is of these a irrational number

a) 3/2

b) $\frac{\sqrt{12}}{\sqrt{3}}$

c) 5.222222……

d) $\frac{\sqrt{12}}{2}$

Solution (d)

8. Which is of these a rational number?

a) 1.234567…..

b) .333333…

c) 1.423153652….

d) None of these

Solution (b)

9) if $x=2+\sqrt{3}$ and $y=\frac{1}{2+\sqrt{3}}$

Then what is the value of x^{2} +y^{2}

a)8

b)10

c) 12

d) 14

Solution ©

__Simplify Following expression__

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