Number Systems(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

NUMBER SYSTEMS MCQs

Total Questions : 197 | Page 2 of 20 pages

Question 11. Which of the following is a rational number?

√2
π
20
4.8

Discuss Question

Answer: Option D. -> 4.8
:
D
A rational numbercan be written in the form of

\frac{p}{q}

where

p

and

q

are integers and

q

is not equal to zero. Rational numbers have their decimal expansions as either terminating or non-terminating but recurring.

π

= 3.14159265358..., i.e., the digits after decimal point do not terminate and not recurring. Hence it is not rational

\sqrt{2}

is approximated to 1.414213562373095..., i.e., it cannot be expressed as a recurring and non-terminating decimal and henceis not rational.

\frac{2}{0}

is not defined and for a rational number, the denominator should be non-zero.
4.8 on the other hand, satisfiesall the properties of rational numbers.

Question 12. The numbers which have a non-terminating and non-repeating decimal expansion or cannot be represented in the form of

\frac{p}{q}

(q is not equal to '0') are known asnumbers.

Discuss Question

:
An irrational numberis a real number that cannot be expressed as a ratio of integers, i.e. as a fraction, where the denominator is different from zero. Therefore, irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat.

\sqrt{2}, \sqrt{3}

are examples of irrational numbers.

Question 13. Every whole number is an/a ___________.

integer
irrational number
(a) and (b) above.
None of the above

Discuss Question

Answer: Option A. -> integer
:
A
Whole numbers comprise the set {0,1,2,3...} whereas integers comprise the set {... -2,-1,0,1,2,...}.
Thus, we can see that whole numbers are a sub-set of integers.
Hence, every whole number is an integer.

Question 14. Which of the following statements is incorrect?

Rational and irrational numbers together make up real numbers
All irrational numbers are real numbers
All real numbers are irrational
Every point on the number line represents a unique real number

Discuss Question

Answer: Option C. -> All real numbers are irrational
:
C
Every irrational number is a real number but real numbers compriseof rational as well as irrational numbers. Moreover, any point on a number line represents a definite real number.

Question 15. Simplify

{(256)}^{\frac{- 1}{2}}

Discuss Question

Answer: Option C. -> 116
:
C
We know that

{(a^{m})}^{n} = a^{m n}

{(256)}^{\frac{- 1}{2}} = {(2^{8})}^{\frac{- 1}{2}} (Since 256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{8})

= 2^{(8 \times (\frac{- 1}{2}))}

= 2^{- 4}

= \frac{1}{16}

Question 16. Rationalising

\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{2}}

will give __________.

5−2√6
5+2√6
7+2√6
7−2√6

Discuss Question

Answer: Option B. -> 5+2√6
:
B
We rationalise the denominator by dividing and multiplying the number by

\sqrt{2} + \sqrt{3}

.
So, we have

\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{2}} \times \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}

= \frac{(\sqrt{3} + \sqrt{2})^{2}}{{\sqrt{3}}^{2} - {\sqrt{2}}^{2}}

= \frac{{(\sqrt{3})}^{2} + {(\sqrt{2})}^{2} + 2 \sqrt{6}}{3 - 2}

[

Using the identity (a + b)^{2} = a^{2} + b^{2} + 2 a b

]

= 5 + 2 \sqrt{6}

Question 17. Which of the following statements is correct?

0 is a natural number
-1 is a whole number
6.5 is an integer
1 is a whole number

Discuss Question

Answer: Option D. -> 1 is a whole number
:
D
Natural numbers start from 1 and continue thereafter by adding 1 each time.
So1, 2,3,4,5... are all natural numbers.
All the natural numbers and "0" together are referred to as whole numbers. Hence 1 is a whole number.
Natural numbers, their negatives and 0 constitute the set of Integers.

Question 18. Which of the following is a rational number between