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A microbiologist measures the speed of a swimming bacterium. The bacterium covers a distance of 6.82 microns in 3.5 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? Use scientific notation and express your answer to the correct number of significant figures. You must show your work for full credit.

Sagot :

Trancescient

Explanation:

Recall that

[tex]1\:\text{micron} = 1\:\mu\text{m} = 10^{-6}\:\text{m}[/tex] so the speed of the bacterium is

[tex]v = \dfrac{6.82×10^{-6}\:\text{m}}{3.5\:\text{s}} = 1.9×10^{-6}\:\text{m/s}[/tex]

Next, we convert this speed to km/hr. Recall that

[tex]1\:\text{km} = 1000\:\text{m}[/tex]

[tex]1\:\text{hr} = 60\:\text{minutes} = 3600\:\text{s}[/tex]

Therefore,

[tex]1.9×10^{-6}\:\dfrac{\text{m}}{\text{s}}×\left(\dfrac{1\:\text{km}}{1000\:\text{m}}\right)×\left(\dfrac{3600\:\text{s}}{1\:\text{hr}}\right)[/tex]

[tex]= 6.8×10^{-6}\:\text{km/hr}[/tex]

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