Download THE NUMBER SYSTEM

Unit 1 The Number System
ACTIVITY 1.7
Evaluate the following:
1
0.3030030003 . . . + 0.1414414441 . . .
2
0.5757757775 . . . – 0.242442444 . . .
3
(3 +
4
2
) × (3 − 2 )
12 ÷ 3
From Example 2 and Activity 1.7, you can generalize the following facts:
i
The sum of any rational number and an irrational number is an irrational number.
ii
The set of irrational numbers is not closed with respect to addition, subtraction,
multiplication and division.
iii
If p is a positive integer that is not a perfect square, then a + b p is irrational
where a and b are integers and b ≠ 0. For example, 3 + 2 and 2 − 2 3 are
irrational numbers.
Exercise 1.3
1
Identify each of the following numbers as rational or irrational:
a
5
6
d
g
3
b
2.34
0.81
e
0.121121112... f
72
h
1+
c
−0.1213141516...
5− 2
3
2
Give two examples of irrational numbers, one in the form of a radical and the
other in the form of a non-terminating decimal.
3
For each of the following, decide whether the statement is 'true' or 'false'. If your
answer is 'false', give a counter example to justify.
a
The sum of any two irrational numbers is an irrational number.
b
The sum of any two rational numbers is a rational number.
c
The sum of any two terminating decimals is a terminating decimal.
d
The product of a rational number and an irrational number is irrational.
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