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Sagot :
We are given the population of Australia and its area. To calculate the number of people per square mile we simply divide as follows
[tex]\frac{\text{population}}{\text{area}}=\frac{2.15\cdot10^7}{2.95\cdot10^{6}}=\frac{2.15}{2.95}\cdot\frac{10^{7}}{10^{6}}[/tex]To calculate this number, first we use the following property
[tex]\frac{10^a}{10^b}=10^{a-b}[/tex]So
[tex]\frac{10^7}{10^{6}}=10^{7-6}=10^1=10[/tex]Then, we have
[tex]\frac{2.15\cdot10^7}{2.95\cdot10^{6}}=\frac{2.15}{2.95}\cdot10[/tex]Note that 2.15 = 215/100 and 2.95=295/100. So we have
[tex]\frac{2.15}{2.95}\cdot10=\frac{\frac{215}{100}}{\frac{295}{100}}\cdot10[/tex]Using the property
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]we get
[tex]\frac{\frac{215}{100}}{\frac{295}{100}}\cdot10=\frac{215\cdot100}{295\cdot100}\cdot10=\frac{215}{295}\cdot10=\frac{43\cdot5}{59\cdot5}\cdot10=\frac{43}{59}\cdot10[/tex]Using a calculator we get
[tex]\frac{43}{59}\cdot10\approx7.28[/tex]so the approximate average number of people per square mile in Australia is 7.28 people per square mile
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