Page 27 - Mathematics

Solution
The following is a list of some irrational numbers.
(i) 2 1.414213562373=  (iv) − 5 = − 2.236067977499

(ii) e = 2.718281828459 (v) 11 3.316624790355= 

(iii) π = 3.141592653589 (vi) − 21 = − 4.582575694956... Tanzania Institute of Education

From these examples, it can be observed that the digits after the decimal point
continue infinitely without repeating.

Note:

The numbers such as ,π e eπ 2,π e π+ , and other similar numbers are
,
,
also called transidentals.

Example 2.11

Given the list of numbers
3 3 3 4 2
−
− 6, 5 , − 4, − , − , 0, , 1, 1 , 8, 3.01, , 8.47. Identify all
π
5 5 8 5 3
irrational numbers in the list.
Solution

The irrational numbers are 8 and . π

Exercise 2.4

1. Determine whether the following are rational or irrational numbers.
Justify your answers.
π
11, 0.65, 12, , 1.101001000100001 , 9, 3+ 7, 3 3 − 5, − 7
2
2
2. Find an irrational number such that x = 7.
3 2
 
−
−
3. Given the numbers 5, 3.5, 0, , 3, 5, 9, − 4.325, π , .
List the numbers which are: 4 2 Mathematics Form One
(a) Whole numbers (c) Rational numbers
(b) Integers (d) Irrational numbers

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Mathematics form 1.indd 21