EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Rational and Irrational Numbers
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Convert the non-terminating recurring decimal
0.33333333333333...
to rational number
(i)
1
(ii)
(
-1
3
)
(iii)
1
3
(iv)
1
5
Question
2
2.
Express
9
10
as a decimal correct to 1 decimal places
(i)
0.7
(ii)
0.8
(iii)
1
(iv)
1.1
(v)
0.9
Question
3
3.
Which of the following is a fifth order surd?
(i)
(
−
6
√
3
)
(ii)
7
5
√
8
(iii)
(
−
3
√
8
)
(iv)
(
−
8
3
√
5
)
(v)
(
−
4
4
√
8
)
Question
4
4.
The decimal number 8.0068 lies between
(i)
{8.0069,8.0070}
(ii)
{8.0048,8.0058}
(iii)
{8.0066,8.0067}
(iv)
{8.0078,8.0088}
(v)
{8.0058,8.0078}
Question
5
5.
Which of the following is a second order surd?
(i)
6
4
√
4
(ii)
(
−
7
√
2
)
(iii)
(
−
9
√
6
)
(iv)
3
3
√
4
(v)
(
−
2
5
√
3
)
Question
6
6.
Express
100
39
as a decimal correct to 3 decimal places
(i)
2.464
(ii)
2.764
(iii)
2.364
(iv)
2.564
(v)
2.664
Question
7
7.
(
−
5
3
√
7
−
5
√
5
+
7
√
8
)
+
(
−
3
√
2
+
√
4
+
3
3
√
9
)
=
(i)
(
−
5
3
√
7
−
5
√
5
+
7
√
8
−
3
√
2
+
√
4
+
3
3
√
9
)
(ii)
(
−
5
3
√
7
−
5
√
5
+
7
√
8
−
3
√
5
+
√
4
+
3
3
√
9
)
(iii)
(
−
5
3
√
7
−
5
√
5
+
7
4
√
8
−
3
√
2
+
√
4
+
3
3
√
9
)
(iv)
(
−
5
3
√
4
−
5
√
5
+
7
√
8
−
3
√
2
+
√
4
+
3
3
√
9
)
(v)
(
−
5
3
√
7
−
5
4
√
5
+
7
√
8
−
3
√
2
+
√
4
+
3
3
√
9
)
Question
8
8.
√
2
13
=
(i)
(
13
2
)
(-1)
(ii)
(
13
2
)
5
(iii)
2
13
(iv)
(
2
13
)
2
(v)
(
13
2
)
2
Question
9
9.
Rationalise the denominator of
1
(
√
7
−
√
8
)
(i)
(
−
√
7
−
2
√
2
)
(ii)
(
−
√
5
−
2
√
2
)
(iii)
(
−
√
7
−
2
4
√
2
)
(iv)
(
−
√
10
−
2
√
2
)
(v)
(
−
√
7
−
4
)
Question
10
10.
Find the rational number at the point labelled with letter M
(i)
86
11
(ii)
88
9
(iii)
28
3
(iv)
86
9
(v)
86
7
Question
11
11.
Simplify
(
−
√
3
)
(
−
√
5
+
√
2
)
+
√
5
(
−
√
6
−
√
7
)
+
(
−
√
3
)
(
√
9
−
√
3
)
(i)
(
1
3
√
15
+
1
3
√
6
+
√
30
−
√
38
−
1
2
√
3
−
1
2
)
(ii)
(
1
3
√
15
+
1
3
4
√
6
+
√
30
−
√
35
−
1
2
√
3
−
1
2
)
(iii)
(
1
3
√
15
+
1
3
√
6
+
4
√
30
−
√
35
−
1
2
√
3
−
1
2
)
(iv)
(
1
3
√
15
+
1
3
√
6
+
√
30
−
√
35
−
1
2
√
3
−
1
2
)
(v)
(
1
3
√
13
+
1
3
√
6
+
√
30
−
√
35
−
1
2
√
3
−
1
2
)
Question
12
12.
Convert the fraction
256
9
to non-terminating recurring decimal
(i)
2.8
4
(ii)
28.
4
(iii)
0.28
4
(iv)
2844.
4
(v)
284.
4
Question
13
13.
6.275 =
(i)
251
4
(ii)
1255
2
(iii)
251
40
(iv)
251
400
(v)
251
4000
Question
14
14.
(
3
√
3
−
4
√
9
+
6
√
8
)
+
(
−
9
√
2
+
8
√
4
−
8
√
6
)
=
(i)
(
3
√
3
+
4
+
3
4
√
2
−
8
√
6
)
(ii)
(
3
√
3
+
4
+
3
√
2
−
8
√
8
)
(iii)
(
3
√
1
3
+
4
+
3
√
2
−
8
√
6
)
(iv)
(
3
√
3
+
5
+
3
√
2
−
8
√
6
)
(v)
(
3
√
3
+
4
+
3
√
2
−
8
√
6
)
Question
15
15.
Which of the following fractions converts to a terminating decimal?
(i)
2856
64
(ii)
259
180
(iii)
259
18
(iv)
164
9
Question
16
16.
Which of the following is a mixed recurring decimal?
(i)
0.33333333333333...
(ii)
29.25925925925925...
(iii)
11.77777777777777...
(iv)
2.77777777777777...
(v)
6.94444444444444...
Question
17
17.
The decimal number 0.623 lies between
(i)
{0,1}
(ii)
{-1,0}
(iii)
{-2,-1}
(iv)
{1,2}
(v)
{2,3}
Question
18
18.
Which of the following symbols represent the set of Irrational numbers ?
(i)
R
(ii)
Z
(iii)
W
(iv)
Q'
(v)
N
Question
19
19.
Find the difference of the rational numbers at the points labelled with letters H and I
(i)
(
-3
2
)
(ii)
(
-1
4
)
(iii)
1
2
(iv)
-1
(v)
(
-1
2
)
Question
20
20.
Which of the following is true?
(i)
37
5
<
21
16
(ii)
24
23
>
23
9
(iii)
37
36
<
37
5
(iv)
32
29
>
23
9
(v)
31
18
<
14
13
Question
21
21.
14
√
2
✕
14
√
9
=
(i)
14
√
21
(ii)
14
√
15
(iii)
14
√
18
(iv)
12
√
18
(v)
16
√
18
Question
22
22.
Express
91
31
as a decimal correct to 1 decimal places
(i)
3
(ii)
2.9
(iii)
3.1
(iv)
2.7
(v)
2.8
Question
23
23.
Express
525
751
as a decimal correct to 3 decimal places
(i)
0.799
(ii)
0.599
(iii)
0.499
(iv)
0.899
(v)
0.699
Question
24
24.
Find the difference of the decimal numbers at the points labelled with letters T and U
(i)
-0
(ii)
0.5
(iii)
0.1
(iv)
0.4
Question
25
25.
Which of the following is true?
(i)
11
18
>
9
11
(ii)
5
9
<
1
4
(iii)
3
17
>
5
18
(iv)
3
4
>
7
13
(v)
5
15
>
9
11
Assignment Key
1) (iii)
2) (v)
3) (ii)
4) (v)
5) (ii)
6) (iv)
7) (i)
8) (v)
9) (i)
10) (iv)
11) (iv)
12) (ii)
13) (iii)
14) (v)
15) (i)
16) (v)
17) (i)
18) (iv)
19) (v)
20) (iii)
21) (iii)
22) (ii)
23) (v)
24) (iii)
25) (iv)
