Scientific Notation problem: The earth is 150,000,000 km from the Sun....

sean1

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Feb 11, 2017
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Hello my friends,
I am very nervous because my final is tomorrow and we barely went over scientific notation and there will be a problem similar to this one we already took on the test. Here was my attempt at it, I was given the answer in class when the professor graded it but I do not understand how to get the answer. Here goes:

The earth is 150,000,000 km from the Sun. There are 1000 meters in a km. How many meters (expressed in scientific notation) is the earth from the sun?

Now, the first number converted to scientific notation is 1.5x10^8. And the amount of meters in a km is 1.0x10^3. The professor gave the answer of 1.5x10^4 but I do not see how she got that. My incorrect answer was 1.5x10^5. Please help, I need all the points on the final that I can get and this should be an easy one :sad:
 

stapel

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The earth is 150,000,000 km from the Sun. There are 1000 meters in a km. How many meters (expressed in scientific notation) is the earth from the sun?

Now, the first number converted to scientific notation is 1.5x10^8. And the amount of meters in a km is 1.0x10^3. The professor gave the answer of 1.5x10^4 but I do not see how she got that.
Me, either! You're starting with a big unit, and going to a smaller unit; so the numbers have to go from a smaller value to a larger value. Since "1.5 × 104" is smaller than the original value of "1.5 × 108", then there's no way that this can be correct!

My incorrect answer was 1.5x10^5.
This is still smaller than the original value, so it can't be correct.

I don't know what steps you used, which led to the above value. If you need only give the answer in scientific notation, then use the regular numbers first:

. . . . .(150,000,000 km)*(1,000 m/km) = 150,000,000,000 m

...because the "km" cancelled off. Then convert this value to scientific notation. ;)
 

sean1

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Feb 11, 2017
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Me, either! You're starting with a big unit, and going to a smaller unit; so the numbers have to go from a smaller value to a larger value. Since "1.5 × 104" is smaller than the original value of "1.5 × 108", then there's no way that this can be correct!


This is still smaller than the original value, so it can't be correct.

I don't know what steps you used, which led to the above value. If you need only give the answer in scientific notation, then use the regular numbers first:

. . . . .(150,000,000 km)*(1,000 m/km) = 150,000,000,000 m

...because the "km" cancelled off. Then convert this value to scientific notation. ;)
You made me see the error of my ways! I read her answer wrong off the board. like you said above it is 1.5 X 10^11 (I read her 11 as a 4.) So it looks like my main issue was I divided when I should have multiplied.
Thanks so much for the help!
 
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