Page 29 - Mathematics

Real numbers

Rational numbers
Irrational numbers Tanzania Institute of Education
Integers

Whole numbers

Natural
numbers

Figure 2.1: Categories of real numbers

If a and b are two real numbers, then either ab= , a is less than b or a is
greater than b. For example, if:

(i) a = 3 and b = 7, then a is less than b or b is greater than a, that is, 3 is
less than 7 or 7 is greater than 3.
12 12
(ii) a = and b = 4, then, ab= that is, = 4.
3 3
3
5,
(iii) a = − and b = − then a is greater than b, that is 3− is greater than
− 5or b is less than a, that is, 5− is less than 3.−
(iv) a – 4 and b 2 then a is less than b, that is – 4 is less than 2 or b
=
=
is greater than a, that is, 2 is greater than 4.−
2
Examples of positive real numbers are 1, 2, 3, , 7, 1.67, and
3
1.020020002  and examples of negative real numbers are:
3
1,
−− 2, − 3, − , − 7, 1.067, 1.020020002− −
2
Note:
1. 0 is also a real number which is neither positive nor negative.
2. Every real number corresponds to a single point on the number line.
3. Every point on the number line corresponds to a certain real number. Mathematics Form One

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Mathematics form 1.indd 23