What is a conversion factor? Think about how units of measure can be represented in different ways.
No, see solution.
Practice makes perfect
We are asked if multiplying by a conversion factor will change the amount of what is being measured, and to explain our reasoning. Let's start by recalling what a conversion factor is.
What Is a Conversion Factor?
A conversion factor is a ratio of two equivalent measures in different units. Some examples are shown below.
Equivalence
Conversion factor
1 foot = 12 inches
1 foot/12 inches
1 yard = 3 feet
1 yardd/3 feet
1 mile = 1760 yards
1 mile/1760 yards
Notice that the quantity of all the numerators and denominators are the same. For example, moving a distance of 1 foot is the same as moving 12 inches. Only the units have changed.
How Does a Conversion Factor Work?
Recall how we simplify the common factors in a fraction.
5x * a/5x * b & = 5x/5x * a/b [1em]
& = 1 * a/b
Using the same logic, we can simplify a conversion factor.
(quantity) (u_1)/(quantity) (u_2) & =quantity/quantity * (u_1)/(u_2)
[1em]
& = 1 * (u_1)/(u_2)
Above, we used u_1 to represent one unit and u_2 to represent a different unit. However, notice that the quantity is the same for both. Then, when multiplying any quantity by a conversion factor this is what happens.
(initial quantity) (u_2) * (quantity) (u_1)/(quantity) (u_2)
The quantity is the same, as we saw before.
(initial quantity) (u_2) * 1 * (u_1)/(u_2)
This can be simplified even further.
(initial quantity)(u_1)
Hence, we can see that multiplying by a conversion factor allows us to change from one unit to another without changing the actual amount of what is being measured.
