For a scale of 1:100,000, how far in miles does 7 7/8” correspond to?

To determine how far 7 7/8 inches corresponds to on a scale of 1:100,000, it's essential to understand what the scale means. A scale of 1:100,000 indicates that 1 unit of measurement on the map (or drawing) represents 100,000 of the same units in reality.

First, convert 7 7/8 inches into a decimal. This can be calculated as follows:

7 7/8 inches = 7 + 7/8 = 7 + 0.875 = 7.875 inches.

Next, apply the scale factor. Since the scale is 1:100,000, each inch on the map corresponds to 100,000 inches in reality. Therefore, to find the real distance, you multiply the measured distance in inches by 100,000:

Real distance = 7.875 inches × 100,000 inches/inch = 787,500 inches.

Now, convert inches to miles. There are 63,360 inches in a mile, so:

Real distance in miles = 787,500 inches ÷ 63,360 inches/mile ≈ 12.42 miles.

Rounding this can yield approximately