11.1: One to One Hundred
A map of a park says its scale is 1 to 100.
- What do you think that means?
- Give an example of how this scale could tell us about measurements in the park.
Let’s explore a different way to express scales.
A map of a park says its scale is 1 to 100.
Your teacher will give you a drawing of the Apollo Lunar Module. It is drawn at a scale of 1 to 50.
The table shows the distance between the sun and 8 planets in our solar system.
planet | average distance (millions of miles) | |
---|---|---|
row 1 | Mercury | 35 |
row 2 | Venus | 108 |
row 3 | Earth | 150 |
row 4 | Mars | 228 |
row 5 | Jupiter | 779 |
row 6 | Saturn | 889 |
row 7 | Uranus | 1,890 |
row 8 | Neptune | 2,800 |
A rectangular parking lot is 120 feet long and 75 feet wide.
In some scale drawings, the scale specifies one unit for the distances on the drawing and a different unit for the actual distances represented. For example, a drawing could have a scale of 1 cm to 10 km.
In other scale drawings, the scale does not specify any units at all. For example, a map may simply say the scale is 1 to 1,000. In this case, the units for the scaled measurements and actual measurements can be any unit, so long as the same unit is being used for both. So if a map of a park has a scale 1 to 1,000, then 1 inch on the map represents 1,000 inches in the park, and 12 centimeters on the map represent 12,000 centimeters in the park. In other words, 1,000 is the scale factor that relates distances on the drawing to actual distances, and $\frac{1}{1,\!000}$ is the scale factor that relates an actual distance to its corresponding distance on the drawing.
A scale with units can be expressed as a scale without units by converting one measurement in the scale into the same unit as the other (usually the unit used in the drawing). For example, these scales are equivalent:
1 inch to 200 feet
1 inch to 2,400 inches (because there are 12 inches in 1 foot, and $200 \boldcdot 12 = 2,\!400$)
1 to 2,400
This scale tells us that all actual distances are 2,400 times their corresponding distances on the drawing, and distances on the drawing are $\frac{1}{2,\!400}$ times the actual distances they represent.