Really confused on this question.
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 must show your work for full credit.
To find the speed of the bacterium in kilometers per hour, we need to convert the distance covered in microns to kilometers, and the time in seconds to hours.
1 micron = 1 x 10^(-6) m
First, let's convert the distance covered by the bacterium from microns to meters:
2.16 microns = 2.16 x 10^(-6) m
Next, let's convert the time from seconds to hours:
5.0 seconds = 5.0 / 3600 hours (since there are 3600 seconds in an hour)
Now we can find the speed of the bacterium by dividing the distance by the time:
Speed = Distance / Time
= (2.16 x 10^(-6) m) / (5.0 / 3600 hours)
= (2.16 x 10^(-6) m) / (5.0 / 3600 hours)
To divide by a fraction, we multiply by the reciprocal:
= (2.16 x 10^(-6) m) x (3600 hours / 5.0)
= (2.16 x 10^(-6) m) x (3600 hours / 5.0)
= (2.16 x 10^(-6) m) x (720 hours)
= 1.5552 x 10^(-3) m/h
Finally, let's convert the speed from meters per hour to kilometers per hour:
1 kilometer = 1000 meters
Speed = 1.5552 x 10^(-3) m/h x (1 km / 1000 m)
= 1.5552 x 10^(-3) km/h
Therefore, the speed of the bacterium is approximately 1.6 x 10^(-3) km/h, when expressed in scientific notation and rounded to the correct number of significant figures.
To find the speed of the bacterium in kilometers per hour, we need to convert the given distance from microns to kilometers and the given time from seconds to hours.
Step 1: Convert the distance from microns to meters.
Given: 1 micron = 1 x 10^(-6) m
Distance in meters = 2.16 microns * (1 x 10^(-6) m/1 micron)
= 2.16 x 10^(-6) m
Step 2: Convert the distance from meters to kilometers.
Given: 1 kilometer = 1000 meters
Distance in kilometers = (2.16 x 10^(-6) m) * (1 km/1000 m)
= 2.16 x 10^(-6) km
Step 3: Convert the time from seconds to hours.
Given: 1 hour = 3600 seconds
Time in hours = 5.0 seconds * (1 hour/3600 seconds)
= 5.0/3600 hours
Step 4: Calculate the speed of the bacterium.
Speed = Distance/Time
= (2.16 x 10^(-6) km)/(5.0/3600) hours
Simplifying the expression:
= (2.16 x 10^(-6) km) * (3600/5.0) / 1 hour
= (2.16 x 10^(-6) km) * (720/1)
= 1.5552 x 10^(-3) km/h
Expressing the final answer to the correct number of significant figures, we have:
Speed of the bacterium = 1.555 km/h
You simply need to express 2.16 micrometres in 5.0 seconds as some kilometres per hour, retaining the appropriate number of significant figures during conversion.
1 μm = 1×10^–6 m
1 km = 1×10^+3 m
1 hr = 3600 s
2.15μm / 5.0s = _._ ×10^__ km/hr