How do we read map scales? How do the units factor into this?
No, see solution.
Practice makes perfect
We are given the scale 1in:100mi, and we are asked if this implies that the actual distance between two towns will be 100 times bigger than the distance on the map. First, let's recall what the scale on a map indicates.
Map scale = Map distance/Actual distance
1 in/100 mi = Map distance/Actual distance
This means that for each inch on the map the actual distance will be 100 miles. However, we cannot compare these distances directly as they are not measured in the same units. We have to convert the miles to inches to have a clearer idea of the map scale. Let's recall the relationships between the given units.
1 mile &= 5280 feet
1 foot &= 12 inches
As we need to cancel out the miles in the denominator of the scale, we will set our conversion factor with miles on the top and feet on the bottom. The second conversion factor will need to have feet on the top — to cancel out with the feet in the previous conversion factor — to obtain inches.
(1mi/5280 ft)(1ft/12 in)
Notice that converting the miles in the denominator of the scale to inches will cause them to cancel out with the inches in the numerator and we will end up with an dimensionless scale, as needed.
1 in/100 mi
(1 mi/5280 ft)(1 ft/12 in) = 1/633604
Therefore, the actual distance between two towns will be 633604 times greater than the distance on the map.
