Which of the following is a unit free scale?

Question

Accepted Answer

The correct answer is Option 2: Representative fraction. Here's why:

*   **Representative Fraction (RF):** The representative fraction is a ratio that expresses the relationship between a distance on a map and the corresponding distance on the ground. It is written as a fraction (e.g., 1/100,000 or 1:100,000). Crucially, the RF is *unitless*. This means that the numerator and denominator are expressed in the *same* units. For example, 1:100,000 means that 1 unit of measurement on the map represents 100,000 of the *same* units on the ground. Whether you're using centimeters, inches, or meters, the ratio remains the same. This unit-free nature makes the RF universally applicable, regardless of the measurement system used.

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

*   **Statement Scale:** A statement scale (also known as a verbal scale) expresses the map scale in words, such as "1 inch equals 1 mile." This scale *explicitly* uses units (inches and miles in this example), making it unit-dependent and therefore not a unit-free scale.

*   **Graphical Scale:** A graphical scale (also known as a bar scale) is a line or bar drawn on the map that represents a specific distance on the ground. While you can use the graphical scale to measure distances without knowing the exact numerical scale, the scale itself is based on specific units (e.g., kilometers, miles) represented by the length of the bar. Therefore, it is not unit-free.

*   **Vernier Scale:** A vernier scale is a device used to obtain precise measurements, often found on instruments like calipers or surveying equipment. It is an auxiliary scale that allows for readings to a fraction of a division on the main scale. It relies on specific units of measurement and is therefore not unit-free.