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 value of \( t = 100 \) seconds, we can follow these steps:

### Step 1: Understand 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 any trailing zeros in a decimal number.

### Step 2: Identify the Given Value
The time taken by the vehicle is given as \( t = 100 \) seconds.

### Step 3: Analyze the Zeros in the Value
In the number \( 100 \):
- The digits '1' and '0' are significant.
- The trailing zeros (the two zeros after '1') can be significant depending on the context of the measurement.

### Step 4: Consider the Least Count
The problem states that the measurement is taken with a stopwatch that has a least count of 1 second. This means that the measurement is precise to the nearest second.

### Step 5: Determine the Significant Figures
Since the least count is 1 second, the zeros in \( 100 \) seconds are considered significant. Therefore, all three digits (1, 0, and 0) are significant.

### Conclusion
The number of significant figures in the value of time \( t = 100 \) seconds is **3**.