All of your steps look good. You seem to understand scientific notation pretty well.
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?
thanks
No, it is an exercise in scale. To show how us how big things really are. The questions ask what is the value of the earth, then the sun, then the solar system, then the milky way, then the local group, then the visible universe. The only thing we have to do is divide the radius of each by the radius of the earth. To get the amount in cents. Then convert that to dollars. So, the earth is worth one penny. .01. Sun is worth 1.09. Solar System is worth 9,407. Now I am trying to figure out the milky way. Which I think is 78 trillion after readjusting.
I have the radius of all given to me on the paper. I just need to divide the radius by 6,378 to get cents.
Milky Way Radius= 50,000 ly
Local Group= 1.5 million ly
visibile universe= 13.7 billion ly
The way Im doing it is converting the light years into kilometers. A light year is 10 trillion km so I multiply that by 1.5 million in the case of the local group. Is this how it should be done?
anyone check my work? milky way=50,000 ly across. 10 trillion km in a light year, so:
5 x 10^4 x 1 x 10^13 = 5 x 10^17.
5 x 10^17 divided by 6.378 x 10^3 =.783 x 10^14
I convert that to 78.3 x 10^12 for the total cents. Now to convert that to dollars I divide 78.3 X 10^12 by 10^2. So I get 78.3 x 10^10 dollars. Which is 783 billion.