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.
2.16µ/s * 1km/10^9µ * 3600s/hr = 7.776x10^-6 km/hr
I am needing help with the same question I am having a hard time putting it in a way my teacher will take it she is very picky on her work.
To convert the speed of the bacterium from microns per second to kilometers per hour, we need to perform the following steps:
Step 1: Convert microns to meters.
Given 1 micron = 1 x 10^(-6) m, we can convert the distance covered by the bacterium from microns to meters:
2.16 microns = 2.16 x 10^(-6) m
Step 2: Convert seconds to hours.
Since we need the speed in kilometers per hour, we need to convert the time from seconds to hours. There are 3600 seconds in an hour, so:
5.0 seconds = 5.0 / 3600 hours
Step 3: Calculate speed in meters per second.
To find the speed in meters per second, we divide the distance (in meters) by the time (in hours):
Speed = (2.16 x 10^(-6) m) / (5.0 / 3600 hours)
Speed = (2.16 x 10^(-6) m) / (5.0 / 3600) hours
Speed = 2.16 x 10^(-6) m x (3600 / 5.0) hours
Speed = 2.16 x 10^(-6) m x 720 hours
Speed = 1.5552 x 10^(-3) m/s
Step 4: Convert meters per second to kilometers per hour.
To convert the speed from meters per second to kilometers per hour, we need to multiply the speed by a conversion factor of 3.6 (since there are 3.6 kilometers in a meter and 1 hour is equal to 3600 seconds):
Speed = (1.5552 x 10^(-3) m/s) x (3.6 km / 1 m) x (3600 s / 1 hour)
Speed = (1.5552 x 10^(-3) m/s) x (3.6 km / 1 m) x (3600 / 1) hour
Speed = 1.5552 x 10^(-3) x 3.6 x 3600 km/hour
Speed = 20.736 km/hour
Therefore, the speed of the bacterium is 20.736 km/hour.
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 taken in seconds to hours. Here's how you can do the conversion step-by-step:
1. Convert microns to meters:
Given: 1 micron = 1 x 10^(-6) m
Distance covered = 2.16 microns
To convert microns to meters, we multiply the distance by the conversion factor:
Distance in meters = 2.16 microns × (1 x 10^(-6) m/1 micron) = 2.16 x 10^(-6) m
2. Convert 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^(-9) km
3. Convert seconds to hours:
Given: 1 hour = 3600 seconds
Time taken = 5.0 s
To convert seconds to hours, we divide the time by the conversion factor:
Time taken in hours = 5.0 s × (1 hour/3600 s) = 1.4 x 10^(-3) hours
4. Calculate the speed:
Speed = Distance/Time = (2.16 x 10^(-9) km) / (1.4 x 10^(-3) hours)
When dividing numbers in scientific notation, we subtract the exponents:
Speed = 2.16 / 1.4 x 10^(-9-3) km/h = 2.16 / 1.4 x 10^(-12) km/h
= 1.54 x 10^12 km/h
Hence, the speed of the bacterium is approximately 1.54 x 10^12 km/h.