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