Understanding Engineering Mathematics

(d) By long division we find:

1

7 =^0.^142857142857 ...=^0.

̇ 142857 ̇

and the string of digits 142857 recur indefinitely as denoted by

the over dots at the ends of the sequence. To six decimal places

we can write

1

7 ^0.^142857

B.(ii) (a) 0. 3 =

3

10

(b) 0. 67 =

67

100

(c) 0. 6 ̇= 0. 6666 ...=^23

To see this, let x= 0. 6666 ...then 10x= 6. 6666 ...and

subtracting gives

9 x= 6

so x=^69 =^23

(d) 3. 142 =

3142

1000

C. (i) 11. 00132 = 1. 100132 × 10

mantissa= 1. 100132

exponent= 1

(ii) 1. 56 = 1. 56 × 100

mantissa= 1. 56

exponent= 0

(iii) 203. 45 = 2. 0345 × 102

mantissa= 2. 0345

exponent= 2

(iv) 0. 0000321 = 3. 21 × 10 −^5

mantissa= 3. 21

exponent=− 5

D.To three significant figures we have

(i) 11. 00132 = 11. 0

(ii) 1.56

(iii) 203. 45 = 203

(iv) 0. 000321 = 0. 000321

1.2.9 Estimation

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531 ➤

With the availability of calculators we are now used to having enormous number crunching
capability at our fingertips. But there are occasions when we don’t have our hands on a