Understanding Engineering Mathematics

1.1.9 Estimation ➤^2531 ➤➤

Estimate the approximate value of each of

(i)

4. 5 × 105 × 2. 0012

8. 892 × 104

(ii)

√

254 × 104 + 28764. 5

2. 01 × 10 − 254 × 10 −^6

1.2 Revision

1.2.1 Types of numbers

➤

227 ➤

Numbers can be classified into different types:

• natural numbers


• zero


• directed numbers


• integers


• rational numbers (fractions)


• irrational numbers


• real numbers


• complex numbers (➤Chapter 12).

The counting numbers

1 , 2 , 3 , 4 ,...

are callednatural numbers.
Zero, 0, is really in a class of its own – we always have to be careful with it. It is an
integer and also, of course, a real number. Essentially, zero enables us to define negative
numbers. Thus, the negative of 3 is the number denotedn=−3 satisfying

3 +n= 0

This enables us to ‘count in opposite directions’ usingdirectedornegative numbers

− 1 ,− 2 ,− 3 ,− 4 ,...

The full set of numbers

{...− 4 ,− 3 ,− 2 ,− 1 , 0 , 1 , 2 , 3 , 4 ,...}

is called the set ofintegers.
Numbers that can be written in the form:

integer

non-zero integer

(

e.g.

3

4

,

− 1

2

)

(

including integers, such as 6=

6

1

)