Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 27
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36MODULE -
1
Number Systems
Algebra
A′
D
C
A
B
O
Notes
P
–2
– 1
0
1
2
= ′
units. Taking O as centre and radius OA′, if we draw an arc, we
∴
+
=
2
2
O
A
1
1
2
reach the point P, which represents the number 2 .
As 2 is irrational, we conclude that there are points on the number line (like P) which
are not represented by a rational number. Similarly, we can show that we can have points
like
etc, which are not represented by rationals.
, 3
2
, 3
5
2
∴ The number line, consisting of points corresponding to rational numbers, has gaps on it.
Therefore, the number line consists of points corresponding to rational numbers and irrational
numbers both.
We have thus extended the system of rational numbers to include irrational numbers also.
The system containing rationals and irrationals both is called the Real Number System.
The system of numbers consisting of all rational and irrational numbers is called the system
of real numbers.
CHECK YOUR PROGRESS 1.5
1. Write the first three digits of the decimal representation of the following:
, 2
, 3
5
2. Represent the following numbers on the real number line:
2
3
+
(i)
(ii)
1
2
(iii)
2
2
1.12 FINDING IRRATIONAL NUMBER BETWEEN TWO
GIVEN NUMBERS
Let us illustrate the process of finding an irrational number between two given numbers
with the help of examples.
Example 1.19:
Find an irrational number between 2 and 3.
Mathematics Secondary Course
29
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