The time taken by a vehicle to go from one station to another is `100` seconds. It is recorded with a stop watch having the least count of `1` second. How many significant figures are there in the value of time `t=100s` ?

Options

A. `3`
B. `4`
C. `2`
D. `1`

Answer

To determine the number of significant figures in the time measurement of `100 seconds`, we need to consider the rules of significant figures, especially in relation to the least count of the measuring instrument used.

### Step-by-Step Solution:

1. **Understanding the Measurement**:
- The time taken by the vehicle is given as `100 seconds`.
- This measurement is recorded using a stopwatch with a least count of `1 second`.

2. **Identifying Significant Figures**:
- Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in a decimal number.
- In the case of `100 seconds`, we have:
- The digit `1` is significant.
- The two zeros following `1` are trailing zeros.

3. **Applying the Rules**:
- Since `100` is a non-decimal number, trailing zeros are not considered significant unless specified otherwise (like in scientific notation).
- Therefore, if we only apply the basic rules, we would count `1` as the significant figure, leading to the conclusion that there is **1 significant figure**.

4. **Considering the Least Count**:
- However, since the measurement was taken with a stopwatch that has a least count of `1 second`, we must consider this aspect.
- The least count indicates the precision of the measurement. Since the stopwatch can measure up to the nearest second, all figures in `100 seconds` are considered significant.
- Thus, we conclude that the number `100` has **3 significant figures** because the least count allows us to consider all digits in this case.

5. **Final Conclusion**:
- Therefore, the total number of significant figures in the measurement of `100 seconds` is **3**.

### Summary:
The number of significant figures in the value of time `t = 100 seconds` is **3**.