Understanding Engineering Mathematics

(x)

18

9

• improper fraction which can be cancelled down to lowest terms as an

integer 2.

(xi) 0.0 – decimal representation, to one decimal place, of zero.

(xii) 0.2 is a decimal fraction expressible as the proper fraction

2

10

=

1

5

.

(xiii) −0.31 is a negative decimal fraction expressible as the negative proper

fraction−

31

100

.

(xiv) 6.3 is a positive decimal number, expressible as the mixed fraction 6

3

10

or

the improper fraction

63

10

.

(xv)

√

3 is a positive irrational number.

(xvi) 3π– irrational.

(xvii) e– irrational.

(xviii) e^2 – irrational.

(xix) −

√

2 is a negative, irrational number.

(xx) −1.371 is a negative decimal fraction expressible as the negative improper

fraction−

1371

1000

.

B. (i) zero (ii) not defined (iii) negative integer

(iv) zero (v) not defined (vi) zero

(vii) not defined (viii) zero (ix) not defined

(x) 4^0 =1(xi)0!= 1 (xii) 24

1.3.2 Use of inequality signs

A. 21 > 11 > 3 π>e^2 > 6. 3 >e>

5

2

> 2

=

18

9

>

√

3 > 1

2

5

>

2

3

> 0. 2 > 0. 0

=− 0 >− 0. 31 >−

3

7

>−

√

2 >− 1. 371 >− 3

B. (i) a^2 <b^2 ≤c^2 (ii)

1

a

>

1

b

≥

1

c

(iii) a+b< 2 c

(iv) −c≤−b<−a (v)

√

a<

√

b≤

√

c

1.3.3 Highest common factor and lowest common multiple

A. (i) 2 is already prime (ii) − 6 =− 1 × 2 × 3 (iii) 21= 3 × 7