`(1101 ms^-1)/(10.2 ms^-1) = 107.94117647 ~~ 108` .

Answer

To solve the problem of why \( \frac{1101 \, \text{ms}^{-1}}{10.2 \, \text{ms}^{-1}} = 107.94117647 \) is equivalent to 108, we will follow these steps:

### Step 1: Perform the Division
First, we need to divide the two values given in the question:

\[ \frac{1101 \, \text{ms}^{-1}}{10.2 \, \text{ms}^{-1}} = \frac{1101}{10.2} \]

Calculating this gives:

\[ \frac{1101}{10.2} = 107.94117647 \]

### Step 2: Identify Significant Figures
Next, we need to determine the number of significant figures in both the numerator and the denominator.

- **Numerator (1101)**: The number 1101 has **4 significant figures**.
- **Denominator (10.2)**: The number 10.2 has **3 significant figures**.

### Step 3: Apply the Rule for Significant Figures in Division
According to the rules of significant figures, when performing division, the result should have the same number of significant figures as the measurement with the least number of significant figures. In this case, the least number of significant figures is **3** (from 10.2).

### Step 4: Round the Result
Now, we need to round the result \( 107.94117647 \) to 3 significant figures.

- The first three significant figures in \( 107.94117647 \) are **107**.
- The next digit (the fourth significant figure) is **9**, which means we round up.

Thus, rounding \( 107.94117647 \) to 3 significant figures gives us:

\[ 108 \]

### Conclusion
Therefore, we conclude that:

\[ \frac{1101 \, \text{ms}^{-1}}{10.2 \, \text{ms}^{-1}} \approx 108 \text{ (to 3 significant figures)} \]

This justifies why we say that \( 107.94117647 \) is equivalent to \( 108 \).

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