A force of 8.26 N is applied normally over an area of `4.2 m^2`. Calculate the pressure exerted over the area to appropriate significant figures.

Answer

To calculate the pressure exerted over an area when a force is applied, we can use the formula:

\[ \text{Pressure} (P) = \frac{\text{Force} (F)}{\text{Area} (A)} \]

### Step-by-step Solution:

1. **Identify the given values**:
- Force \( F = 8.26 \, \text{N} \)
- Area \( A = 4.2 \, \text{m}^2 \)

2. **Substitute the values into the pressure formula**:
\[ P = \frac{F}{A} = \frac{8.26 \, \text{N}}{4.2 \, \text{m}^2} \]

3. **Perform the division**:
\[ P = \frac{8.26}{4.2} \approx 1.964285714 \, \text{N/m}^2 \]

4. **Determine the appropriate significant figures**:
- The force \( 8.26 \, \text{N} \) has 3 significant figures.
- The area \( 4.2 \, \text{m}^2 \) has 2 significant figures.
- Therefore, the final answer should be reported with 2 significant figures (the least number of significant figures).

5. **Round the result to 2 significant figures**:
- The calculated pressure is approximately \( 1.964285714 \, \text{N/m}^2 \).
- Rounding this to 2 significant figures gives \( 2.0 \, \text{N/m}^2 \) (since the third digit is 6, we round up).

### Final Answer:
The pressure exerted over the area is \( 2.0 \, \text{N/m}^2 \).

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