STATEMENT 1 When the unit for measurement of a quantity is changed, its numerical value changes
STATEMENT 2 Smaller the unit of measurement matter is its numerical value

Options

A. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To analyze the two statements given in the question, let's break down each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** "When the unit for measurement of a quantity is changed, its numerical value changes."

- **Understanding the Statement:** This statement is addressing the relationship between the unit of measurement and the numerical value of a quantity.
- **Example:** Consider a length of wire that measures 1 meter. If we convert this length into centimeters, we know that:
\[ 1 \text{ meter} = 100 \text{ centimeters} \]
- **Conclusion for Statement 1:** The quantity (length of wire) remains the same, but the numerical value changes from 1 (meter) to 100 (centimeters). Thus, this statement is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** "Smaller the unit of measurement, greater its numerical value."

- **Understanding the Statement:** This statement suggests that as the unit of measurement becomes smaller, the numerical value associated with that measurement increases.
- **Example:** Using the same example, we have:
- 1 meter = 100 centimeters
- **Comparison of Units:** Here, the meter is a larger unit compared to the centimeter. When we use a smaller unit (centimeter), the numerical value increases from 1 to 100.
- **Conclusion for Statement 2:** The statement implies that smaller units always yield greater numerical values, which is not universally true. For instance, if we consider millimeters:
\[ 1 \text{ meter} = 1000 \text{ millimeters} \]
Here, the numerical value is even greater. However, the statement does not hold true in all contexts, especially when comparing different quantities. Therefore, this statement is **false**.

### Final Conclusion
- **Statement 1:** True
- **Statement 2:** False