Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 25
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36MODULE -
1
Number Systems
Algebra
∴ We have been able to find 3 rational numbers
9
10
11
1
3
,
and
between
and
16
16
16
2
4
Notes
In fact, we can find any number of rationals between two given numbers.
1
50
50
=
=
Again
×
2
2
50
100
×
3
3
25
75
=
=
×
4
4
25
100
50
51
52
53
72
73
74
75
<
<
<
<
<
<
<
<
<
.....
....
As
(i)
100
100
100
100
100
100
100
100
1
3
∴ we have been able to find 24 rational numbers between
and
as given in
2
4
(i) above.
We can continue in this way further.
Note:
From the above it is clear that between any two rationals an infinite number of
rationals can be found.
CHECK YOUR PROGRESS 1.4
1. Find a rational number between the following rational numbers:
3
4
3
1
−
(i)
and
(ii)
5
and
6
(iii)
and
4
3
4
3
2. Find two rational numbers between the following rational numbers:
2
1
2
1
−
−
(i)
–
and
(ii)
and
3
2
3
4
3. Find 5 rational numbers between the following rational numbers:
(i) 0.27 and 0.30
(ii) 7.31 and 7.35
(iii) 20.75 and 26.80
(iv) 1.001 and 1.002
Mathematics Secondary Course
27
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