Topic Content:
- Word Problems with Large & Small Numbers
Worked Example 8.4.1:
Given that x = 85 000, and y = 25 000 find the value of
a. \( \scriptsize x \: + \: y \)
b. \( \scriptsize x \: \times \: y \)
c. \( \scriptsize x \: \div \: y \)
Give your answer in standard form.
Solution
a. x + y = \( \scriptsize 85\:000 \: + \: 25\:000\\ \scriptsize = 170\:000 \\ \scriptsize = 1.7 \: \times \: 10^5 \)
b. x × y = \( \scriptsize 85\:000 \: \: \times \: \: 25\:000\\ \scriptsize = 8.5 \: \times \: 10^4 \: \times \: 2.5 \: \times \: 10^4 \\ \scriptsize = 21.25 \: \times \: 10^4 \: \times \: 10^4 \\ \scriptsize = 21.25 \: \times \: 10^{4\:+\:4}\\ \scriptsize = 21.25 \: \times \: 10^{8}\\ \scriptsize but \: 21.25 = 2.125 \: \times \: 10^1 \\ \scriptsize =\left( 2.125 \: \times \: 10^1\right) \: \times \: 10^8 \\ \scriptsize = 2.125 \: \times \: 10^{1\:+\:8}\\ \scriptsize = 2.125 \: \times \: 10^9 \)
c. x ÷ y = \( \frac{x}{y} \\= \frac{85\not{0}\not{0}\not{0}}{25 \not{0}\not{0}\not{0}} \\= \frac{85}{25} \\= \frac{17}{5} \\ = \scriptsize 3.4 \\ = \scriptsize 3.4 \: \times \: 10^0\)
Worked Example 8.4.2:
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.
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