Let's solve the problems in the image step by step, ensuring that all results are expressed in the standard form of scientific notation with five significant figures.

1. Sum of Measured Distances

You need to sum the following distances: 13.50 m, 9.220 m, and 0.875 m.

$\text{Sum} = 13.50 + 9.220 + 0.875 = 23.595 \text{ m}$

Since the least number of decimal places in the measurements is 3 (from 0.875 m), the result should be rounded to three decimal places:

$\text{Sum} = 23.595 \text{ m}$

In scientific notation with five significant figures:

$\text{Sum} = 2.3595 \times 10^1 \text{ m}$

2. Force Applied by a Truck

The force $F$ is calculated using the formula:

$F = m \times a$

Given:

• Mass $m = 9.31 \times 10^4 \text{ kg}$
• Acceleration $a = 2.5 \times 10^{-2} \text{ m/s}^2$

$F = (9.31 \times 10^4) \times (2.5 \times 10^{-2}) = 23.275 \times 10^2 \text{ N}$

Converting to scientific notation with five significant figures:

$F = 2.3275 \times 10^3 \text{ N}$

3. Density of an Unknown Object

Density $\rho$ is given by the formula:

$\rho = \frac{m}{V}$

Given:

• Mass $m = 5.3 \times 10^{-2} \text{ kg}$
• Volume $V = 1.10 \times 10^2 \text{ m}^3$

$\rho = \frac{5.3 \times 10^{-2}}{1.10 \times 10^2} = 4.8182 \times 10^{-4} \text{ kg/m}^3$

In scientific notation with five significant figures:

$\rho = 4.8182 \times 10^{-4} \text{ kg/m}^3$

4. Total Area of Carpet Needed

The area $A$ of the carpet is calculated using the formula:

$A = \text{length} \times \text{width}$

Given:

• Length = 5.664 m
• Width = 4.5 m

$A = 5.664 \times 4.5 = 25.488 \text{ m}^2$

In scientific notation with five significant figures:

$A = 2.5488 \times 10^1 \text{ m}^2$

5. Volume of a Wooden Box

The volume $V$ of the box is calculated using the formula:

$V = \text{length} \times \text{width} \times \text{height}$

Given:

• Length = 12.10 cm = 0.1210 m
• Width = 18.998 cm = 0.18998 m
• Height = 30 cm = 0.3000 m

$V = 0.1210 \times 0.18998 \times 0.3000 = 0.006914 \text{ m}^3$

In scientific notation with five significant figures:

$V = 6.9140 \times 10^{-3} \text{ m}^3$

Would you like to dive into any of these calculations or have any further questions? Here are some related questions to consider:

1. How does the precision of measurements affect the number of significant figures in a calculated result?
2. Why is it important to express results in scientific notation in physics and engineering?
3. Can you explain the difference between accuracy and precision in measurements?
4. How do you determine the correct number of significant figures in multiplication and division?
5. What are some common mistakes when rounding off numbers to significant figures?

Tip: Always ensure your final answers reflect the correct number of significant figures based on the precision of the given data.