Question

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. (1 point)

Answer 1

To find the total length of the two insects, we need to add their lengths together, which are given in scientific notation:

1. The length of the first insect is \(4 \times 10^{-2}\) inches.
2. The length of the second insect is \(1.3 \times 10^{-1}\) inches.

To add these numbers together, we'll first convert them to the same power of ten. It’s easier to convert \(1.3 \times 10^{-1}\) to \(10^{-2}\):

\[
1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10^{1}}{10^{1}} = 1.3 \times 10^{1} \times 10^{-2} = 13 \times 10^{-2}
\]

Now we can add the two lengths together:

\[
4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2}
\]

Next, we convert \(17 \times 10^{-2}\) to proper scientific notation by expressing 17 as \(1.7 \times 10^{1}\):

\[
17 \times 10^{-2} = 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1}
\]

Therefore, the total length of the two insects is:

\[
\boxed{1.7 \times 10^{-1}} \text{ inches.}
\]