Sometimes, when we are choosing an appropriate unit, we are not given any formula to use.
This often occurs when we measure the rate of change of something. A rate of change measures how much something changes as we change something else.
In such cases, we can use a quotient to work out an appropriate unit. The numerator is what we measure the change of, and the denominator is what we change:
For instance, suppose that a newly opened store wants to measure the rate at which the number of customers increases each day.
We measure the change of the number of customers, as we change the number of days, so the most appropriate unit is or, customers per day.
A tank is being filled with water. What is an appropriate unit for measuring the rate of change of water volume in the tank, as time goes on?
We measure the change of the volume as we change the amount of time. Consequently, any appropriate unit for measuring the rate of change of water volume in the tank must take the form
Some examples of appropriate units include and
Vova launches a plowing business. He wants to know how the area of plowed land changes as the volume of fuel he uses increases. What is an appropriate unit for Vova's purpose?
|
a
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liters per hour |
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b
|
liters per meter |
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c
|
square meters per liter |
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d
|
square meters per hour |
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e
|
liters per square meter |
Jenny, a swimmer, is training for a tournament. She wants to measure the number of meters that she swims in a certain time interval. What is an appropriate unit for Jenny's purpose?
|
a
|
Strokes per meter |
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b
|
Meters per stroke |
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c
|
Seconds per meter |
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d
|
Meters per second |
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e
|
Meters per pool |
Density is the rate that mass changes as volume changes. What are the units of density in terms of base units?
We measure the change in the mass, as we change the volume. Consequently, any appropriate unit must take the form
The base unit for mass is and the base unit for volume is Therefore, the units of density are or, kilograms per cubic meter.
John is filling a bathtub. He wants to determine how the volume of water changes as time goes on. What are appropriate units for John's purpose, in terms of base units?
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a
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$\dfrac{\textrm{s}}{\textrm{m}}$ |
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b
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$\dfrac{\textrm{m}^2}{\textrm{s}}$ |
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c
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$\dfrac{\textrm{m}}{\textrm{s}}$ |
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d
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$\dfrac{\textrm{m}^3}{\textrm{s}}$ |
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e
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$\dfrac{\textrm{s}}{\textrm{m}^3}$ |
A biologist is growing bacteria in a petri dish. She wants to measure how the mass of bacteria changes as she changes the area of the dish that is covered in sugar coating. What are appropriate units for her purpose, in terms of base units?
|
a
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$\dfrac{\textrm{kg}}{\textrm{m}}$ |
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b
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$\dfrac{\textrm{m}^2}{\textrm{kg}}$ |
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c
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$\dfrac{\textrm{kg}}{\textrm{m}^2}$ |
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d
|
$\dfrac{\textrm{kg}}{\textrm{m}^3}$ |
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e
|
$\dfrac{\textrm{m}}{\textrm{kg}}$ |