Teacher gave us this for extra credit. He wants us to convert astronomical objects into money based on their radius. This is how it works. The earth is worth one penny. $.01
The earth's radius is 6,378 km. So 6,378 km equal one penny in this system.
Next we move on to the sun, which has a radius of 696,000 km. So we divide that by 6,378. Which is 109 cents. So the sun is worth 1.09
Solar System is 40 AU. I want this in km. AU is 1.5 x 10^8 km. So do 40 times 1.5 x 10^8 =6,000,000,000km or 6 x 10^9. So then I divide 6 x 10^9 by 6.378 x 10^3. And I get 940,733 cents. Drop 2 decimals to convert to dollars and I get $9,407 for the price of the solar system.
I know the final answers on those are correct because he helped us with him.
It is the even bigger ones I am having problems with. Next is Milky Way. It is 50,000 light years across. I want to convert this to km too. A light year is 10 trillion km. So I multiply 50,000 by 10 trillion. Or is there a better way to do this? Anyway, assuming I do multiply them it is 5 x 10^4 x 1 x 10^13. So that is 5 x 10^17. Now I divide this by 6.378 x 10^3 and get .78394481 x 10^14. Now what? Should I get rid of some exponents? Maybe 783 x 10^9? Which is 78,300,000,000,000 cents. Take out to points to convert to dollars and you have $783,000,000,000 as the cost of the Milky Way, Is this correct? Is there a better way to do it?