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

Answers:

2

5

5.4

6.5

10^-8

10^-2

10^2

10^6

Answer 1

To find the total decrease in water level over 1.8 × 10^4 seconds, we can use the following calculation:

Decrease in water level per second: \(3.6 \times 10^{-2}\) mm/second

Total decrease in water level over time: \[ (\text{Decrease per second}) \times (\text{Total seconds}) = (3.6 \times 10^{-2} , \text{mm/second}) \times (1.8 \times 10^{4} , \text{seconds}) \]

Calculating it step by step:

1. Multiply the coefficients: \[ 3.6 \times 1.8 = 6.48 \]

2. Add the exponents (since both are in scientific notation): \[ 10^{-2} \times 10^{4} = 10^{(-2 + 4)} = 10^{2} \]

Combining both parts: \[ 6.48 \times 10^{2} \]

Now convert \(6.48\) to scientific notation: \[ 6.48 = 5.4 \times 10^{0} \implies \text{or } 6.5 , \text{is} , \text{for simplicity} \]

Thus, we rewrite it appropriately as: \[ 6.5 \times 10^{2} \]

So, the final answer can be expressed as: \[ 6.5 \times 10^{2} , \text{mm} \]

Now, to fill in the response areas based on the selected values:

Response area: 6.5
Response area: 10^2
Response area: mm

So the correct selections would be:

• 6.5 for the first response area
• 10^2 for the second response area
• mm at the end.