Lesson 8, Topic 4
In Progress

# Word Problems with Large & Small Numbers

Lesson Progress
0% Complete

### Example 1

Given that x = 85 000, and y = 25 000 find the value of

a. $$\scriptsize x \: + \: y$$

b. $$\scriptsize x \: \times \: y$$

c. $$\scriptsize x \: \div \: y$$

Solution

a. x  + y    =   85 000  +  25 000

=   170 000

=  1.7 x 105

b. x ×  y   =   85 000  x  25 000

=  8.5 x 104   x  2.5 x 104

= 8.5 x 2.5 x 104 x 104

= 21. 25 x 104 x 104

= 21.25 x 104+4

= 21. 25 x 108

= But 21.25 = 2.125 x 101

= (2.125 x 101) x 108

= 2.125 x 101+8

= 2.125 x 109

c. x ÷ y   = $$\frac{x}{y} \\= \frac{85\not{0}\not{0}\not{0}}{25 \not{0}\not{0}\not{0}} \\= \frac{85}{25} \\= \frac{17}{5} \\ = \scriptsize 3.4 \\ = \scriptsize 3.4 \: \times \: 10^0$$

### Example 2

The population of Nigeria is about 145 million and the population of Britain is about 58 million. Write these numbers in standard form and find the difference in population between the two countries.

Solution

Nigeria = 145 million

= 145 x 1 000 000

= 145  x 106

but 145 = 1.45 x 102

Therefore,

= (1.45 x 102) x 106

= 1.45 x 102+6

= 1.45 x 108

Britain = 58  million

= 58 x 1 000 000

= 58 x 106

but 58 = 5.8 x 101

Therefore,

= (5.8 x 101) x 106

= 5.8 x 101+6

=  5.8 x 107

Difference in population  =  145 million  – 58 million

= 87 million

= 87 x 1 000 000

= 87 x 106

but 87 = 87 x 101

Therefore,

= (8.7 x 101) x 106

= 8.7 x 101+6

= 8.7 x 107

Evaluation Questions:

1. Give the following to

i.    1.sf
ii.    2s.f
iii.    3s.f
iv.    4.s.f

a.    289 959
b.    25.5299

2. Give the following to:

i.    1s.f
ii.    2s.f
iii.    3s.f
iv.    4s.f.

a.    0.000 058 819
b.    0.070 938
c.    0.45734

3.    Round off the following to the nearest whole number

a.    84. 27
b.    580. 718
c.    0.755
d.    19.99

4.    Round off each of the following:

a.    ₦259.85 to the nearest
b.    539.35mm to the nearest mm
c.    569.78m to the nearest 100m
d.    7825.2 litres to the nearest 10 litres

5a.    The distance of the earth from the sun is 148 729 440 000 m.  Express this distance in km, in standard form, giving your answers correct to 3.s.f.

b.    The universal constant of gravitation is given as G = 0.000 000 000 066 73m3/kg.s2.  Write  this number in standard form correct to 2 s.f..

c.    ₦275 million was used to buy 50 houses. If the prices of thee houses are the same. Calculate the cost of one house, giving your answer correct to 1 s.f.

#### Responses error: