What is the conversion of statement scale of "1 inch represents 8 miles" into RF?

Question

Accepted Answer

The correct answer is Option 4: 1 : 506,880. Here's why:

To convert the statement scale "1 inch represents 8 miles" into a Representative Fraction (RF), we need to express both sides of the ratio in the same units. Since RFs are unitless, we need to convert miles to inches.

*   **Step 1: Convert miles to feet:** 1 mile = 5280 feet. Therefore, 8 miles = 8 * 5280 = 42,240 feet.

*   **Step 2: Convert feet to inches:** 1 foot = 12 inches. Therefore, 42,240 feet = 42,240 * 12 = 506,880 inches.

*   **Step 3: Express as RF:** The statement "1 inch represents 8 miles" now translates to "1 inch represents 506,880 inches." This can be written as the RF 1 : 506,880.

Therefore, Option 4 is the correct RF representation of the given statement scale.

Now, let's explain why the other options are incorrect:

*   **Option 1: 1 : 570,240:** This value is incorrect because it represents a different conversion factor from miles to inches than the one derived above. It doesn't accurately reflect the 8 miles to inches conversion.

*   **Option 2: 1 : 380,160:** This value is also incorrect. It likely arises from an error in the conversion process, perhaps using an incorrect number of feet in a mile or inches in a foot.

*   **Option 3: 1 : 443,520:** This value is incorrect for the same reason as options 1 and 2. The calculation to convert 8 miles into inches was not performed correctly to arrive at this value.