I must show my work for full credit. I need help on this question. I don't need answers, but could you help me figure it out.

Question

Thanks

A microbiologist measures the speed of a swimming bacterium. The bacterium covers a distance of 2.16 microns in 5.0 seconds. The biologist wished to compare the speed of the bacteria with other animals, but the speeds of other animals are listed in kilometers per hour. What is the speed of the bacterium in kilometers per hour? (1 micron = 1 x 10–6 m) Use scientific notation and express your answer to the correct number of significant figures.

Answer 1

You are not understanding the factor label method using unit factors.
Note these
1micron=1E=6 m
or 1 = 1E-6 m/micron=1micron/1E-6 m
notice that is a unity factor (equal to 1)
also note
1000m=1km or
1=1km/1000m = 1000m/1km
Now, because you can multiply anything in an equation by ONE... then
speed=distance/time=2.16microns/5 seconds

now, we start multiplying by UNIT factors to divide out the units. Starting with the microns in the numerator..
speed=2.16microns/5s * 1E-6m/micron
microns divides out, now you have left meters/second
then, multiply to get the meters do change to km. Multiply by 1km/1000m
so now the units are meters/second.

Now, seconds to hours. 3600s=1hr or
1=1hr/3600s= 3600s/hr

because you have seconds in the denominator, you want to multply speed you have in km/s by (3600s/hr)

and you are done. The trick is to write this down, with the UNITS attached, so you see they do in fact cancel. You cant use a calculator to do this. So wait until you have got the units where you need them, then get the calc. Then you should have this...

(2.16/5)(1e-6/1)(1/1000)(3600/1) CHECK THAT.

Answer 2

Thanks, I was not really understanding the factor label method until now, this helped out a lot. I appreciate it.