Question

The population of australia is 2.15*10⁷ The area of Australia is 2.95*10⁶ square miles. What is the approximate average number of people per square mile in Australia?

Answer 1

We are given the population of Australia and its area. To calculate the number of people per square mile we simply divide as follows

`\frac{\text{population}}{\text{area}}=(2.15\cdot10^7)/(2.95\cdot10^(6))=(2.15)/(2.95)\cdot(10^(7))/(10^(6))`

To calculate this number, first we use the following property

`(10^a)/(10^b)=10^(a-b)`

So

`(10^7)/(10^(6))=10^(7-6)=10^1=10`

Then, we have

`(2.15\cdot10^7)/(2.95\cdot10^(6))=(2.15)/(2.95)\cdot10`

Note that 2.15 = 215/100 and 2.95=295/100. So we have

`(2.15)/(2.95)\cdot10=((215)/(100))/((295)/(100))\cdot10`

Using the property

`((a)/(b))/((c)/(d))=(a\cdot d)/(b\cdot c)`

we get

`((215)/(100))/((295)/(100))\cdot10=(215\cdot100)/(295\cdot100)\cdot10=(215)/(295)\cdot10=(43\cdot5)/(59\cdot5)\cdot10=(43)/(59)\cdot10`

Using a calculator we get

`(43)/(59)\cdot10\approx7.28`

so the approximate average number of people per square mile in Australia is 7.28 people per square mile