Question

The map of Colorado scale says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same?

Answer 1

Map scales can be expressed either as a ratio or graphically (inches to miles). To convert between map measurements and actual distances, ratios and proportions are used.

Step-by-step explanation:

Yes, the two ways of reporting the scale are equivalent. The scale is typically expressed in two ways: a verbal scale (such as "1 inch to 20 miles") and a representative fraction (such as "1:1,267,200"). These two representations convey the same information about the relationship between the distance on the map and the actual distance on the ground.

In this case:

Verbal Scale: "1 inch to 20 miles" means that each inch on the map represents 20 miles in reality.

Representative Fraction: "1:1,267,200" is a ratio that indicates the same relationship. The first number (1) represents the distance on the map, and the second number (1,267,200) represents the corresponding distance on the ground. Therefore, 1 unit on the map is equivalent to 1,267,200 units on the ground.

Both representations convey the idea that distances on the map are 1/1,267,200th of the actual distances on the ground, and as such, they are the same scale reported in different ways.