Converting a simple scale (also known as a verbal scale or statement scale) to a ratio scale (also known as a representative fraction) involves expressing the relationship between a map distance and the corresponding distance on the ground as a fraction or ratio. Here's how you do it:
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Understand the Simple Scale: A simple scale is a statement like "1 inch equals 4 kilometers." This means one unit of measurement on the map represents a certain distance on the ground.
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Convert Units to the Same Measurement: The key step is to ensure that both sides of the statement are in the same unit of measurement. You will likely need to convert the ground distance (e.g., kilometers, miles) to the map distance's unit (e.g., inches, centimeters).
- Example: Using the video's example, we start with "1 inch equals 4 kilometers". We need to convert 4 kilometers to inches.
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Conversion Factors: You'll need to know the appropriate conversion factors. Some common ones include:
- 1 kilometer = 1000 meters
- 1 meter = 100 centimeters
- 1 inch = 2.54 centimeters (approximately)
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Perform the Conversion:
- Continuing the example, convert 4 kilometers to centimeters: 4 km 1000 m/km 100 cm/m = 400,000 cm
- Convert centimeters to inches: 400,000 cm / 2.54 cm/inch = 157,480.31 inches (approximately).
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Express as a Ratio: Now that both sides are in the same unit (inches in this case), express the relationship as a ratio. The ratio scale is Map Distance : Ground Distance.
- So, 1 inch on the map represents approximately 157,480.31 inches on the ground. Therefore, the ratio scale is approximately 1:157,480.
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Simplify (Optional): Depending on the context, you may round the ratio scale for ease of use (e.g., 1:160,000).
In summary, the process involves:
- Starting with a simple scale statement (e.g., 1 cm = 10 km).
- Converting both map distance and ground distance to the same unit of measurement.
- Expressing the result as a ratio (e.g., 1:1,000,000).
