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.
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.
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.
Thanks, I was not really understanding the factor label method until now, this helped out a lot. I appreciate it.
To convert the speed of the bacterium from microns per second to kilometers per hour, we need to perform a few steps.
Step 1: Convert microns to meters.
1 micron = 1 x 10^(-6) meters (given in the question)
To convert 2.16 microns to meters, we multiply by the conversion factor:
2.16 microns * (1 x 10^(-6) meters/1 micron) = 2.16 x 10^(-6) meters
Step 2: Convert seconds to hours.
There are 3600 seconds in 1 hour (60 seconds/minute * 60 minutes/hour).
To convert 5.0 seconds to hours, we multiply by the conversion factor:
5.0 seconds * (1 hour/3600 seconds) = 5.0 / 3600 hours
Step 3: Calculate the speed in meters per second.
To calculate the speed, we divide the distance (in meters) by the time (in hours).
Speed = Distance / Time
Speed = (2.16 x 10^(-6) meters) / (5.0 / 3600 hours)
Step 4: Convert meters per second to kilometers per hour.
1 kilometer = 1000 meters
1 hour = 3600 seconds
To convert the speed from meters per second to kilometers per hour, we multiply by the conversion factor:
Speed = (2.16 x 10^(-6) meters) / (5.0 / 3600 hours) * (1000 meters/1 kilometer) * (1 hour/3600 seconds)
Speed = (2.16 x 10^(-6) * 1000) / 5.0 kilometers per hour
Finally, we can calculate the speed of the bacterium in kilometers per hour:
Speed = (2.16 x 10^(-6) * 1000) / 5.0
= (2.16 x 10^(-3)) / 5.0
= 0.432 x 10^(-3)
= 4.32 x 10^(-4) kilometers per hour
Therefore, the speed of the bacterium is 4.32 x 10^(-4) kilometers per hour.
Sure, I can help you figure out the answer without directly giving it to you.
To find the speed of the bacterium in kilometers per hour, we need to convert the distance traveled and the time taken into the appropriate units.
First, let's convert the distance from microns to kilometers. We know that 1 micron is equal to 1 x 10^(-6) meters. To convert microns to kilometers, we can use the following conversion factor:
1 kilometer = 10^3 meters
Since we have the distance in microns, we need to convert it to meters and then to kilometers.
2.16 microns * (1 x 10^(-6) m/1 micron) * (1 km/10^3 m) = ?
Simplifying this calculation, we find the distance covered by the bacterium in kilometers.
Next, we need to convert the time taken from seconds to hours. We know that 1 hour is equal to 3600 seconds. To convert seconds to hours, we can use the following conversion factor:
1 hour = 3600 seconds
5.0 seconds * (1 hour/3600 seconds) = ?
Simplifying this calculation, we find the time taken in hours.
Finally, to find the speed in kilometers per hour, we can divide the distance covered in kilometers by the time taken in hours.
Speed = Distance/Time
Now you have all the necessary information. I will let you plug in the numbers and perform the final calculation to find the speed of the bacterium in kilometers per hour. Make sure to use scientific notation and express your answer to the correct number of significant figures.