Basic Decimals Problem

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Basic Decimals Problem

by missrochelle » Sun Aug 15, 2010 9:40 pm
Someone pls tell me what I'm missing here --

OG #28. The average distance between the sun and a certain plant is approximately 2.3 x 10^14 inches. Which of the following is closes to the the average distances in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches).

A) 7.1 x 10^8
B) 5.9 x 10^9
C) 1.6 x 10^10
D) 1.6 x 10^11
E) 5.9 x 10^11

OA: B


I cross multiplied , ending up with:
2.3/3.9 x 10^10 this is correct
then estimated 2/4 * 10^10 again--- correct
back to decimal form since that's the format of the answer choices .... gives me .5 x 10^10

this is where i get lost.
in order to convert .5 to 5, you have to factor the expression by 10^1. That gives me E .

Please explain how 10^-1 times .5 = 5. I have re-read the rules over and over and i get .5 * 10^-1 (move 1 decimal to the left) leads me to .05.
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by selango » Sun Aug 15, 2010 10:18 pm
3.9*10^4 inches=1 km

2.3*10^14 inches=x km

x=2.3*10^14/3.9*10^4

=2.3/3.9*10^10

=2/4*10^10

=0.5*10^10
in order to convert .5 to 5, you have to factor the expression by 10^1. That gives me E .
=0.5*10*10^9

=5*10^9
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by Prashantbhardwaj » Sun Aug 15, 2010 10:54 pm
You don't need to calculate much in this question really.

Distance in inches is 2.3*10^14
1km = 3.6*10^4

So simply dividing to find km

2.3/3.9 * 10^14/10^4

2.3/3.9 * 10^10

Since 2.3 < 3.9
therefore the answer will be with x.x * 10^9