Using a very precise measuring device, Dr. Calvin measured the thickness of a piece of metal to be 0.00064 of a meter. Dr. Amos measured another piece to be 2.5 × 10^-5 of a meter thick.

Question

If the doctors put the two pieces of metal on top of each other, the new piece of metal would be Blank × 10^-4 of a meter thick.

Answer 1

To find the total thickness of the two pieces of metal when stacked on top of each other, we need to add the two measurements together. The thicknesses are:

• Dr. Calvin's measurement: \(0.00064\) meters
• Dr. Amos's measurement: \(2.5 \times 10^{-5}\) meters

First, we will convert \(0.00064\) meters into scientific notation to make it easier to add the two measurements: \[ 0.00064 = 6.4 \times 10^{-4} \text{ meters} \]

Now we have:

• \(6.4 \times 10^{-4}\) meters (from Dr. Calvin)
• \(2.5 \times 10^{-5}\) meters (from Dr. Amos)

Next, we need to express \(2.5 \times 10^{-5}\) in terms of \(10^{-4}\) so we can add it to \(6.4 \times 10^{-4}\): \[ 2.5 \times 10^{-5} = 0.25 \times 10^{-4} \text{ meters} \]

Now we can add the two measurements: \[ 6.4 \times 10^{-4} + 0.25 \times 10^{-4} = (6.4 + 0.25) \times 10^{-4} = 6.65 \times 10^{-4} \text{ meters} \]

Thus, the total thickness of the two pieces of metal when stacked together is: \[ 6.65 \times 10^{-4} \text{ meters} \]

So, filling in the blank in your question, the answer is: \[ \text{6.65} \] Finally, the entire answer is \( \text{6.65} \times 10^{-4} \text{ meters} \).