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31 votes
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?

User Jwhazel
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1 Answer

13 votes
13 votes

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

User Jnv
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