1. Which of the following rational numbers have terminating decimal representation?

3 2 40 23
A) B) C) D)
5 13 27 7

2. How many rational numbers can be found between two distinct rational numbers?
(A) Two (B) Ten (C) Zero (D) Infinite

3. (27)-2/3 is equal to

(A)9 (B)1/9 (C) 3 (D) none of these

4. Select the correct statement from the following

7 4 2 3 −2 −4 −5 −3
(A) > (B) < (C) > (D) <
9 5 6 9 3 5 7 4

5. 7. 2 is equal to

68 64 65 63
(A) (B) (C) (D)
9 9 9 9
6. A terminating decimal is

(A) a natural number (B) a rational number (C ) a whole number (D)an integer

p
7. The form of the number 0.8 is
q
8 8 1
(A) (B) ( C) (D) 1
10 100 8

3 2
8.The rational number not lying between and
5 3

49 50 47 46
(A) (B) (C) (D)
75 75 75 75

9. 0.123 is equal to

122 122 122

(A) (B) (C) (D)none of these
90 100 99
10. The value of 0. 23+0. 22 is

(A) 0.45 (B)0.4 4 (C)0. 45 (D) 0. 44

11 .Which of the following is a rational number?

(A)√ 4 (B)√ 3(C)√ 14 (D)√ 5

12.A terminating decimal is

(A)natural number (B) a whole number (C) a rational number (D)an integer

−1 −2
13.The rational number between and is
5 5

−1 −3 −7
(A)0 (B) (C) (D)
4 10 25

2
∧5
14.Two rational numbers between 3
are
3

1 5 2
1 2 ∧2 ∧7 ∧4
(A) and (B) 2 (C) 6 (D) 3
6 6
7 6 3

15.The multiplicative inverseof -1 is

(A)1 (B)-1 (C) 10 (D) -10

1 1 −5
16. X ¿)= X x +y X ,then
2 2 12
3 1 1 3 3 5 1 2
(A)x= ,y= (B)x= ,y= (C)x= ,y= (D)x= ,y=
4 2 2 4 2 12 3 5

17.which of the following is correct ?

2 41 4 2 4 41 2 41 4 41 2 4
(A) > > (B) < < (C) < <¿ (D) < <
3 60 5 3 5 60 3 60 5 60 3 5

6
18.The additive inverse of is
8

−6 −8 6 8
(A) (B) (C) (D)
8 6 8 6

−7
19.If x= , then - (-x)=
8

7 −7 8 −8
(A) (B) (C) (D)
8 8 7 7

20. If
−4 5 −8
X( X
5 7 9
)=
−4
5
Xk X
−8
9 ( )
, then k is equal to
 −5 5 4
(A) (B) (C) (D)None of these
7 7 7

21.Can we write 0 in the form of p/q ?

(A) yes (B) No (C) cannot be explained (D) None of these

22.Every rational number is

(A)whole number (B)Natural number (C)Integer (D) Real Number

23.which of the following is true?

(A)Every whole number is a natural number (B)Every integer is a rational number

(C)Every rational number is an integer (D)Every integer is a whole number

24.which of the following is not a rational number.

(A)1.5 (B)2.477 (C)1.277 (D)π

1
25.4 in decimal form is
8

(A)4.125 (B)4.15 (C)4.15 (D)0. 415

26.The sum of 0.5+0. 2

7 7 7 7
(A) (B) (C) (D)
10 9 99 11

27.Decimal representation of a rational number cannot be

(A)terminating (B)non-terminating (C)non-terminating and repeating (D)non-terminating andnon

repeating

28.what is the reciprocal of 0.6?

5 3 4 2
(A) (B) (C) (D)
3 4 5 7

29.which of the following is a rational number?

(A) √5 (B) π (C) 0. 101001000100001……….(D)0.853853853………

15 5 7 2
30.( + ¿ ÷( − )=
16 4 12 3
 −4 105 −105 4
(A) (B) (C) (D)
105 4 4 105

31.The decimal fractionin in which there are finite number of digits in its decimal part is called

(A)terminating decimal fraction (B)non-terminating decimal fraction

(C)linear fraction (D)quadratic fraction

p
32.calculate the form of 0.777, where p and q are integers and q≠ 0
q

7 8 6 9
(A) (B) (C) (D)
9 9 7 7

33.The product of a rational and an irrational number is

(A)Always an integer (B)Always a rational number (C)Always an irrational number (D)Sometimes

rational and sometimes irrational

34.The three rational numbers between 3 and 4 are

5 6 7 13 14 15 12 13 14 11 12 13
(A) , , (B) , , (C) , , (D) , ,
2 2 2 4 4 4 7 7 7 4 4 4

−20
35.The product of two numbers is . If one of the numbers is 4, find the other.
9

−5 3 12 −9
(A) (B) (C) (D)
9 11 39 11

36.A rational number between √ 2∧√ 3 is

(A)
√2+ √3 (B)
√2−√ 3 (C) 1.5 (D)1.8
2 2

37.Which of the following is a rational number?

4 0
(A) (B) (C) both (A) and (B) (D)None
0 4

38.A rational number between -2 and 6 is given by

(A)−2>2>6 (B)-2<2<6 (C)-2>2>6 (D)-2<2>6

p
39.A rational number is of form, where q
q
(A)=1 (B)=-1 (C)=0 (D)≠ 0

16
40.The decimal representation of is
45

(A) 0.35 (B) 0. 35 (C) 0.35 (D)0.035

41.A terminating decimal is

(A)Natural number (B)a Whole number (C)a rational number (D) an Integer

56
42. The decimal form of is
1000

(A)0.56 (B)0.056 (C)0.0056 (D)5.6

43.Which of the following is a rational number?

2 4
(A) (B) (C) √ 1.2 (D)0.32
√3 √5
44.Which of the following number is rational

6 5 √6
(5+√ 5 ¿(5−√ 5)
2
(A) ( √ 2+2) (B) (C) (D)
2 √3 √2
45.Which of the following is not a rational number

(A) (B)0 (C) √4 (D)√ −16

46.Which of the following is commutative for rationalnumbers?

(A)Addition and Subtraction (B) Addition and Multiplication

(C)Multiplication and Division (D)Subtraction and Division

−10 −15 17
47.The value of X X x0
3 2 19

(A)0 (B)20.66 (C)20 (D)35)

48.Reciprocal of -2 is

−1 2
(A) -2 (B) (C) 1 (D)
2 3

1
49.Multiplicative inverse of is
8
 2 2
(A)7 (B) (C)8 (D)
7 8

50. X
7
8 ( 1713 + 1413 )=¿) +( 78 X −¿
−17 17 34 −34
(A) (B) (C) (D)
13 13 13 13

SAQ (2 Marks)

p
1) Express 0.47 in the form of , where p and q are integers and q≠ 0
q
p
2) Express 0.88888………in the form of
q
p
3)Express3.651 in the form of , where p and q are integers and q≠ 0
q
3) Find the four rational numbers between 3 and 4
x
4) If =0.6+ 0. 4 , find the value of x.
9
5) Find the rational number midway between the given numbers.
−1 −1 1 3
(a) and (b) and
2 3 2 4
−4 −5 1 −21
8)Subtract the sum of and from the sum of and
7 3 2 22
7 5 11 −1 −3
9)Arrange the rational numbers , , , , in ascending and descending order
9 6 12 3 4
5
∧6
10.Find three rational numbers between 7
7
p
11.Is zero a rational number? Can you write it in the form of , where p and q are integers and
q
q≠ 0

12.
Long Answer Questions 4 marks

1) Write the following in decimal form and say what kind of decimal expansion each has
36 1 1 3
a) b) c) 4 d)
100 11 8 13

1 2 3 4 5 6
2) You know that = 0.142857 . can you predict what the decimal expansions of , , , , are,
7 7 7 7 7 7
without actually doing the long division? If so, how?
 p
3) Express each of the following in form
q

(a)0.7 (b) 0.32 (c)23. 47 (d)1.3 4

4) Visualise 4.28 on the number line upto 4 decimal places.

p
5)Express each of the following decimal numbers in the form :
q

(i)6.0025 (ii)25.75 (iii)-28.6875 (iv)0.225

3Marks

10 7 1
1) Find the decimal representations of , and
3 8 7
p
2) Show that 1.272727……=1.27 can be expressed in the form , where p and q are integers and q
q
≠0
3 4
3) Find five rational numbers between and
5 5
p
4) Express each of the following pure recurring decimals in the frorm
q
(a)0.6 (b)0.585 (c)23. 43
5) Draw a number line and represent thefollowing on it.
−7 14 −11
(a) (b) (c)
8 10 6
p
6)convert the following decimal numbers in the form (a) 5.2 (b)23. 43
q

11)
Fill in the blanks

3
1)Decimal representation of is ----------
4

22
2)Decimal representation of is-----------
7

23
3)Decimal representation of is -----------
16

4)If we divide 5 by 8 and a finite number of steps, the remainder becomes zero. Such a decimal
expansion is known as ------------

5)A number written in the form of -------------is called a rational number.

6)The decimal representation of a rational number is either------------or-------------

7)A rational number is either----------------in nature or ----------------in nature

8)0. 46 is equal to ----------

9)The simplest form of 23. 43 is---------

10)A decimal in which all the digits are repeated after the decimal point is known as--------

11)A decimal in which atleast one of the digits after the decimal point is not repeated and some digits
are repeated is known as----------

a
12)The additive inverse of is ---------
b

13)The numbers repeating in decimal places is called------------

14) The number of digits repeating in decimal places is called-----------

TRUE/FALSE
1)Rational number is either terminating or non-terminating in nature

p 7
2) form of 0.35 is
q 30

3)Every rational number is an integer

p 2
4)The form of 0.6 is
q 3

5)The sum of a rational number and an irrational number is irrational

−2
∧1 −5
6)A rational number between 3 is
24
4

7)
√2 is a rational number
3

8)Between two rational numbers there are infinitely many rational numbers

9)Zero is a rational number

10)Every integer is a rational number

MATCH THE FOLLOWING

Matching Columns

Match the columns in each of the following:

columnA ColumnB

413
1. (a)1.692307
999

2
2. (b)-0.3
15
 22
3. (c)0. 413
13

1
4.- (d)0.13
3

46
5. (e)0. 46
99

Match the following

1. Closure property (a)ax(bxc)=(axb)xc

2. Commutative property (b)ax(b+c)=(axb)+(axc)
3. Additive Identity (c)a+0=0+a=a
4. Associative property (d)a+b=b+a
5. Distributive property (e)a+b=c is also a rational number

Match the following in each of the following:

ColumnA ColumnB

8
1.(i) (a)0.13
3

16
2.(ii) (b)2.6
45

4
3 (iii). (c)0.35
9

2
4.(iv) (d)0. 4
15

6
5.(v) (e)0.54
11