EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Rational and Irrational Numbers
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
The multiplicative inverse of
(
-6
5
)
is
(i)
(
-1
5
6
)
(ii)
1
6
(iii)
(
-5
6
)
(iv)
(
-2
5
6
)
(v)
1
1
6
Question
2
2.
(
−
4
√
3
)
+
(
−
2
√
3
)
=
(i)
(
−
6
√
5
)
(ii)
(
−
6
4
√
3
)
(iii)
(
−
6
√
3
)
(iv)
(
−
18
)
(v)
(
−
6
)
Question
3
3.
Rationalise the denominator of
1
(
5
√
5
−
5
√
3
−
3
√
4
)
(i)
(
−
35
5302
√
5
−
215
5302
√
3
−
246
2653
−
75
2651
√
15
)
(ii)
(
−
35
5302
√
5
−
215
5302
√
3
−
246
2651
−
75
2651
√
15
)
(iii)
(
−
35
5302
√
5
−
215
5302
4
√
3
−
246
2651
−
75
2651
√
15
)
(iv)
(
−
35
5302
√
5
−
215
5302
√
3
−
246
2651
−
75
2651
√
18
)
(v)
(
−
35
5302
√
3
−
215
5302
√
3
−
246
2651
−
75
2651
√
15
)
Question
4
4.
(
9
3
√
5
−
4
3
√
8
+
3
3
√
2
)
−
(
4
√
6
+
2
√
8
−
5
3
√
6
)
=
(i)
(
9
3
√
5
−
4
3
√
8
+
3
5
√
2
−
4
√
6
−
2
√
8
+
5
3
√
6
)
(ii)
(
9
3
√
2
−
4
3
√
8
+
3
3
√
2
−
4
√
6
−
2
√
8
+
5
3
√
6
)
(iii)
(
9
3
√
5
−
4
3
√
8
+
3
3
√
2
−
4
√
9
−
2
√
8
+
5
3
√
6
)
(iv)
(
9
3
√
5
−
4
3
√
8
+
3
3
√
2
−
4
√
6
−
2
√
8
+
5
3
√
6
)
(v)
(
9
3
√
5
−
4
5
√
8
+
3
3
√
2
−
4
√
6
−
2
√
8
+
5
3
√
6
)
Question
5
5.
Find the difference of the decimal numbers at the points labelled with letters U and V
(i)
-0.1
(ii)
0.6
(iii)
0.3
(iv)
0.7
(v)
0.1
Question
6
6.
Which of the following is a pure recurring decimal?
(i)
17.72222222222222...
(ii)
24.27777777777777...
(iii)
0.43333333333333...
(iv)
0.33333333333333...
Question
7
7.
The decimal number -8.0007 lies between
(i)
{-8.0017,-7.9997}
(ii)
{-8.0027,-8.0017}
(iii)
{-8.0009,-8.0008}
(iv)
{-8.0006,-8.0005}
(v)
{-7.9997,-7.9987}
Question
8
8.
Which of the following decimal numbers lie between
7887.329
and
7887.330
?
(i)
7887.3297
(ii)
78873.2971
(iii)
7887.3289
(iv)
788.733
(v)
7887.3309
Question
9
9.
Convert the fraction
197
21
to non-terminating recurring decimal
(i)
938.
095238
(ii)
9.
380952
(iii)
93.
809523
(iv)
0.09
380952
(v)
0.9
380952
Question
10
10.
Which of the following is an irrational number?
(i)
30.2381
(ii)
√
72
(iii)
8
(iv)
3
13
(v)
6
Question
11
11.
3
√
9
✕
3
√
7
=
(i)
√
5105
(ii)
√
5101
(iii)
√
5103
(iv)
5103
(v)
4
√
5103
Question
12
12.
Express
99
100
as a decimal correct to 2 decimal places
(i)
0.1
(ii)
1.09
(iii)
9.9
(iv)
0.79
(v)
0.99
Question
13
13.
Find the product of the rational numbers at the points labelled with letters G and H
(i)
464
23
(ii)
506
25
(iii)
544
27
(iv)
504
25
(v)
502
25
Question
14
14.
Simplify
√
8
(
−
√
5
−
√
4
)
−
√
9
(
√
2
+
√
5
)
−
√
4
(
√
3
+
√
4
)
(i)
(
−
2
√
10
+
5
√
2
−
4
√
5
+
2
√
3
−
4
)
(ii)
(
−
2
√
10
+
5
√
2
−
√
5
+
2
√
5
−
4
)
(iii)
(
−
2
√
10
+
5
√
2
−
√
5
+
2
√
3
−
4
)
(iv)
(
−
2
√
10
+
5
4
√
2
−
√
5
+
2
√
3
−
4
)
(v)
(
−
2
√
7
+
5
√
2
−
√
5
+
2
√
3
−
4
)
Question
15
15.
Find the rational number at the point labelled with letter H
(i)
23
11
(ii)
23
9
(iii)
7
3
(iv)
25
9
(v)
23
7
Question
16
16.
Express
1
9
as a decimal correct to 2 decimal places
(i)
0.11
(ii)
0.01
(iii)
1.11
(iv)
-0.09
(v)
0.21
Question
17
17.
Rationalise the denominator of
(
−
4
√
8
−
3
√
9
)
(
−
4
√
2
+
2
√
3
)
=
(i)
(
14
5
+
9
5
√
2
+
4
5
√
6
+
9
10
√
3
)
(ii)
(
16
5
+
9
5
√
2
+
4
5
√
6
+
9
10
√
3
)
(iii)
(
16
5
+
9
5
√
2
+
4
5
√
6
+
9
10
√
5
)
(iv)
(
16
5
+
9
5
√
2
+
4
5
4
√
6
+
9
10
√
3
)
(v)
(
16
5
+
9
5
4
√
2
+
4
5
√
6
+
9
10
√
3
)
Question
18
18.
Which of the following decimal numbers lie between
8913.7237
and
8913.7238
?
(i)
8913.72382
(ii)
8913.72362
(iii)
89137.23733
(iv)
891.37237
(v)
8913.72373
Question
19
19.
Which of the following is a fifth order surd?
(i)
(
−
7
√
9
)
(ii)
8
√
6
(iii)
(
−
4
4
√
7
)
(iv)
(
−
8
5
√
4
)
(v)
(
−
3
3
√
6
)
Question
20
20.
(
9
√
6
−
2
3
√
8
+
2
√
7
)
+
(
2
3
√
7
−
7
3
√
6
+
3
√
5
)
=
(i)
(
9
√
3
−
2
3
√
8
+
2
√
7
+
2
3
√
7
−
7
3
√
6
+
3
√
5
)
(ii)
(
9
√
6
−
2
5
√
8
+
2
√
7
+
2
3
√
7
−
7
3
√
6
+
3
√
5
)
(iii)
(
9
√
6
−
2
3
√
8
+
2
√
7
+
2
3
√
10
−
7
3
√
6
+
3
√
5
)
(iv)
(
9
√
6
−
2
3
√
8
+
2
4
√
7
+
2
3
√
7
−
7
3
√
6
+
3
√
5
)
(v)
(
9
√
6
−
2
3
√
8
+
2
√
7
+
2
3
√
7
−
7
3
√
6
+
3
√
5
)
Question
21
21.
Convert the fraction
520
21
to non-terminating recurring decimal
(i)
247.
619047
(ii)
24.
761904
(iii)
2476.
190476
(iv)
2.
476190
(v)
0.2
476190
Question
22
22.
Which of the following decimal numbers lie between
4844.08
and
4844.09
?
(i)
484.409
(ii)
48440.883
(iii)
4844.088
(iv)
4844.075
(v)
4844.093
Question
23
23.
1.339 =
(i)
1339
100000
(ii)
1339
1000
(iii)
1339
10
(iv)
1339
10000
(v)
1339
100
Question
24
24.
Which of the following is a decimal fraction?
(i)
8
5
(ii)
7
17
(iii)
18
4
5
(iv)
7
100
(v)
9
5
9
Question
25
25.
The decimal number 1.084 lies between
(i)
{1.085,1.086}
(ii)
{1.082,1.083}
(iii)
{1.094,1.104}
(iv)
{1.064,1.074}
(v)
{1.074,1.094}
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (iv)
5) (v)
6) (iv)
7) (i)
8) (i)
9) (ii)
10) (ii)
11) (iii)
12) (v)
13) (iv)
14) (iii)
15) (ii)
16) (i)
17) (ii)
18) (v)
19) (iv)
20) (v)
21) (ii)
22) (iii)
23) (ii)
24) (iv)
25) (v)
