Useful material for answering Q1 and Q2

Key distance conversions:

Conversions between different units of measurement are also an important part of scale and distance calculations.

Key conversions are listed below:

• 1 inch = 2.54 centimeters
• 1 statute mile = 5,280 feet = 63,360 inches
• 1 statute mile = 1.609 kilometers
• 1 kilometer = 100,000 centimeters
• 1 nautical mile = 6,076.1 feet
• 1 foot = 12 inches
• 1 meter = 100 centimeters

Explanation of representative fraction

Map scale is defined as the mathematical relationship between a unit of distance on the map and its corresponding distance on the ground. The ratio of map distance to ground distance, both in the same units of measurement, is called the representative fraction (RF) for the map. It is computed from the following equation:

1/X = map distance (md) / ground distance (gd)

We will use this equation in the following scale problems. Hence, an RF of 1/24,000 means that 1 centimeter on the map represents 24,000 centimeters on the ground, 1 inch on the map represents 24,000 inches on the ground, and so on for other units of distance measurement. The RF can also be written as 1:24,000.

MAP SCALE QUESTIONS

Q1: Convert the following representative fractions into a word statement:

(Hint; your answer to the parts a, b and c of this question should be something like: "One inch on the map is equal to x feet on the ground")

a) Express the scale of a large-scale map with an RF of 1:5,000 (1 inch to .... feet)

b) Do the same for a medium-scale map with an RF of 1:25,000 (1 inch to.... statute miles)

c) And for a small-scale map with an RF of 1:10,000,000 (1 inch to .... statute miles)

Q2: On a map of 1:50,000 scale, the distance measured between points A and B is 5.3 inches. What ground distance in statute miles, nautical miles, and kilometers does this represent? (3.0 points)

a) Statute miles:

b) Nautical miles:

c) Kilometers:

Q3: On a map of 1:20,000 scale, you are asked to draw a fence that is 3 statute miles long. How many inches of fence will you have to draw on the map?