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CBSE - Class 9 Mathematics Number Systems Worksheet

1.

How many factors 120 have?

a.

12

b.

8

c.

16

d.

none of these

2.
Write the following in decimal form and say what kind of decimal expansion each has :
(iii) $4\frac{1}{8}$
3.

Whole Number is defined as {0} + N, where N is Set of all Natural Numbers. ie {0,1,2,3,4,5,…..}

a.

TRUE

b.

FALSE

4.

Which list contains only irrational numbers

a.

√2, √3, √4, √5, √6, √7, √8

b.

√2, √3, √255, √6, √7, √8

c.

√2, √3, √5, √6, √7, √8, √256

d.

√2, √69, √6, √7, √81.1

5.
State True/False: If the product of two surds is a rational number, then each one of them is called the rationalising factor of the other.
a. true b. false
6.

If x = , then find the value of qx2-2px+q

7.

Are the cube roots of all positive integers irrational?

a. True b. False
8.
Write 62/100 in decimal form.
9.
Simplify each of the following expressions:
(i) $(3 + \sqrt{3})(2 + \sqrt{2})$
10.
Choose the correct option: Which of the following is irrational?
a. 0.14000000000000001 b. 0.1416 c. 0.1416 d. 0.4014001400014…
11.
Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$?
12.

Every integer is rational number

a. True b. False
13.

Adding 3√2+5√5 and -2√5-2√2, we get

a.

√2-3√5

b.

√2+3√5

c.

-√2+3√5

d.

5√2+7√5

14.

10 Rational numbers between 1/2 & 1/3 are 0.51,0.52,0.53,0.54,0.56,0.57,0.58,0.59,0.60 & 0.61

a.

TRUE

b.

FALSE

15.

1/18 & 5/23 are equivalent fractions (or equivalent rational numbers)

a.

TRUE

b.

FALSE

16.

Simplify and express the result in the simplest form - (25)3/2 * (243)2/5 / (16)5/4 * (8)4/3?

17.

1/2=0.5 - TRUE or FALSE

18.

Definition of Rational Number based on decimal expansion of numbers

a.

All the numbers, whose decimal expansion are either 'Terminating' or 'Not Terminating but Recurring'

b.

All the numbers, whose decimal expansion are 'Terminating'

c.

All the numbers, whose decimal expansion are either 'Terminating' or 'Not Terminating Not Recurring'

d.

All the numbers, whose decimal expansion are Not Terminating but Recurring'

e.

All the numbers, whose decimal expansion are 'Not Terminating Not Recurring'

19.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$? Perform the division to check your answer.
20.

(-5+2√5-√5) is

a. an irrational number b. a positive rational number c. a negative rational number d. an integer

Worksheet Answers

1.
Option C

Solution:

total factors of 120= 16

3.
Option A
4.
Option B
5.
Option A

6.

0

7.
Option B

Solution:

The cube root of a perfect cube is always a rational number. 


8.
0.62
10.
Option D
12.
Option A
13.
Option B
14.
Option B
15.
Option B

16.

(1125/512)

18.
Option A
20.
Option A

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