Which of the following statements is correct about conversion of units, for example `1m = 100 cm` ?

Options

A. Conversion of units have identical dimensions on each side of the equal sign but not the same units.
B. Conversion of units have identical dimensions on each side of the equal sign but not the same units.
C. If a larger unit is used then numerical value of physical quantity is large.
D. Due to conversion of units physical quantity to be measured will change.

Answer

To determine which statement is correct about the conversion of units, we need to analyze the statements based on the example given: \(1 \text{ m} = 100 \text{ cm}\).

### Step-by-step Solution:

1. **Understanding Unit Conversion**:
- When converting units, we are essentially expressing the same physical quantity in different units. In this case, both meters and centimeters measure length.

2. **Identical Dimensions**:
- The first statement claims that "conversion of units have identical dimensions on each side." This is true because both meters (m) and centimeters (cm) are units of length, which means they share the same dimension (denoted as \(L\) for length).

3. **Different Units**:
- The first statement also acknowledges that while the dimensions are the same, the units themselves are different (m and cm). This is correct, as they are different units of measurement for the same dimension.

4. **Evaluating Other Statements**:
- The second statement suggests that "conversion of units have identical dimensions on each side of the equal sign but not the same units." This is essentially a rephrasing of the first statement and is also correct, but it doesn't add new information.
- The third statement claims that "if a larger unit is used, then the numerical value of the quantity is large." This is incorrect. For example, \(1 \text{ km} = 1000 \text{ m}\) shows that using a larger unit (kilometers) results in a smaller numerical value (1 instead of 1000).
- The fourth statement states that "due to conversion of units, the physical quantity to be measured will change." This is incorrect. The physical quantity remains the same; only the units change.

5. **Conclusion**:
- The only correct statement regarding unit conversion is the first one: "conversion of units have identical dimensions on each side."

### Final Answer:
The correct statement about the conversion of units is: **"Conversion of units have identical dimensions on each side."**