Dimensional analysis. Conversion factor confusion

 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.)
Mentor
P: 40,947
 Quote by Edin_Dzeko 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.)
You have a misplaced decimal point in your answer, but that could be left over from Paint.

Still, I don't know why the teacher's answer isn't 5.23*10^5cm...
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,474 Hint: 1 m = 100 cm
P: 23,536
Dimensional analysis. Conversion factor confusion

 Quote by SteamKing Hint: 1 m = 100 cm
That's equivalent to 1cm = 0.01m, both give perfectly valid conversion factors.

5.23x105 cm it is, there is a mistake in the given answer.

 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.
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,474 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.
Mentor
P: 40,947
 Quote by Edin_Dzeko 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.
Looks like your teacher accidentally did 3.21 miles instead of 3.25 miles.

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