A leak in a water tank causes the water level to decrease by 3.6×10−2

Question

millimeters each second.

About how many millimeters does the water level in the tank decrease in 5 hours, or 1.8×104
seconds?



Drag and drop the values to the boxes to express the answer in scientific notation.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Response area × Response area mm

Answer 1

To find the total decrease in the water level over 5 hours (or 18,000 seconds), we can perform the following calculation:

1. Determine the decrease per second: \[ \text{Decrease per second} = 3.6 \times 10^{-2} \text{ mm/s} \]

2. Determine the total time: \[ \text{Total time} = 18,000 \text{ seconds} = 1.8 \times 10^4 \text{ seconds} \]

3. Calculate the total decrease: \[ \text{Total decrease} = \text{Decrease per second} \times \text{Total time} = (3.6 \times 10^{-2}) \times (1.8 \times 10^4) \]

4. Perform the multiplication: \[ = 3.6 \times 1.8 \times 10^{-2 + 4} = 6.48 \times 10^{2} \]

5. Express in scientific notation: Since \(6.48\) is not in the standard format for scientific notation (which requires a leading digit smaller than 10), we rewrite it as: \[ 6.48 \times 10^{2} = 6.48 \times 10^2 \text{ mm} = 6.48 \times 100 \text{ mm} = 648 \text{ mm} \] However, to retain the scientific notation form, we must convert \(6.48\) appropriately: \[ 6.48 = 6.48 \times 10^0 \quad \text{(if needed)} \] Thus, we finalize it as: \[ \approx 6.48 \times 10^2 mm \]

Final answer:

• Select 6.48 for the first response area.
• Select 2 for the second response area.
• Therefore, the decrease in the water level is approximately \(6.48 \times 10^2 \text{ mm}\).