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Dimensional analysis. Conversion factor confusion 
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#1
Jun1311, 05:50 PM

P: 223

1. The problem statement, all variables and given/known data
How many centimeters are there in 3.25 miles? 2. Relevant equations So basically, convert 3.25 mi to cm. 3. The attempt at a solution Uploaded with ImageShack.us The teacher put the answer for this problem as 5.16 x 10^5 The teacher used: (1609 m/1 mile)(100 cm/ 1 m) as her conversion factor. Why / how is mine wrong? I used the metric prefixes system to get my conversion factor numbers. ****(This was done with MS Paint so please disregard the 3rd grader hand writing.) 


#2
Jun1311, 06:01 PM

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Still, I don't know why the teacher's answer isn't 5.23*10^5cm... 


#3
Jun1411, 03:11 AM

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Hint: 1 m = 100 cm



#4
Jun1411, 05:12 PM

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Dimensional analysis. Conversion factor confusion
5.23x10^{5} cm it is, there is a mistake in the given answer. Even google agrees. 


#5
Jun1411, 05:34 PM

P: 223

Okay. Thanks guys. This clears it up.
Here's an exact copy and paste of what the teacher's response was: 3.25 miles (1609 m/1 mile)(100 cm/ 1 m) = 5.16 X 10^5 cm So my conversion factor wasn't off. I guess it might have been a mistake. 


#6
Jun1411, 08:08 PM

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The larger point is, by using the conversion 1 cm / 0.01 m in the calculation, the poster multiplied 5229.25 m by 1 cm / 0.01 m. The poster then cancelled the 'm' units and neglected to apply the factor '0.01' in the denominator of the conversion factor. If the poster had used the conversion factor 1 m = 100 cm, it should have been readily apparent that the magnitude of the result in cm should be greater than the measurement in m.



#7
Jun1411, 08:53 PM

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Did you move the decimal point in your answer in time to get full credit? 


#8
Jun1511, 02:13 AM

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