A certain insect is approximately 4×10^2 inches long. A second insect is about 1.3×10^−1 inches long. What is the total length of the two insects in inches? Use scientific notation to express your answer to 1 decimal place.

Answer 1

To find the total length of the two insects, we need to add their lengths together.

1. The length of the first insect is: \[ 4 \times 10^2 = 400 \text{ inches} \]

2. The length of the second insect is: \[ 1.3 \times 10^{-1} = 0.13 \text{ inches} \]

Now, we add the two lengths together: \[ 400 + 0.13 = 400.13 \]

Next, we need to express this total length in scientific notation. The total length \(400.13\) can be rewritten in scientific notation as follows: \[ 400.13 = 4.0013 \times 10^2 \]

To round to one decimal place in scientific notation: \[ 4.0013 \approx 4.0 \text{ (to 1 decimal place)} \]

Thus, the total length expressed in scientific notation is: \[ \boxed{4.0 \times 10^2} \]