The problem provided involves calculating the upper bound for the area of a rectangle. Let's go through it step by step.

Given:

• The length of the rectangle is $25.0 \, \text{cm}$ (correct to the nearest cm).
• The width of the rectangle is $9.6 \, \text{cm}$ (correct to the nearest 0.1 cm).

Step 1: Determine the Upper Bound of the Length and Width

1. Upper Bound for Length:

   • The length is $25.0 \, \text{cm}$, correct to the nearest cm.
   • The upper bound for the length is $25.0 + 0.5 = 25.5 \, \text{cm}$.

2. Upper Bound for Width:

   • The width is $9.6 \, \text{cm}$, correct to the nearest 0.1 cm.
   • The upper bound for the width is $9.6 + 0.05 = 9.65 \, \text{cm}$.

Step 2: Calculate the Upper Bound of the Area

• The area $A$ of a rectangle is given by: $A = \text{length} \times \text{width}$

• The upper bound for the area: $A_{\text{upper}} = 25.5 \times 9.65 = 246.075 \, \text{cm}^2$

Final Answer:

• The upper bound for the area of the rectangle is 246.075 cm².
• You should write down all the figures on your calculator display, which would be 246.075.

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:

1. What is the lower bound of the area of the rectangle?
2. How would the area change if the length was measured with a precision of 0.1 cm?
3. Can you calculate the perimeter of the rectangle using the upper bound values?
4. What is the percentage error when using the upper bound instead of the exact measurements?
5. How would you calculate the area if only the diagonal of the rectangle was given?

Tip: When calculating with bounds, always adjust the values by half of the smallest unit of measurement used for accuracy.