To find the total length of the two insects, we need to add their lengths together:
- The length of the first insect: \(4 \times 10^{-2}\) inches
- The length of the second insect: \(1.3 \times 10^{-1}\) inches
To add these two numbers, it is helpful to express them with the same exponent.
Convert \(1.3 \times 10^{-1}\) to have the same exponent as \(4 \times 10^{-2}\):
\[ 1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10^{-1}}{10^{-1}} = 1.3 \times 10^{-1} = 13 \times 10^{-2} \]
Now, we can add \(4 \times 10^{-2}\) and \(13 \times 10^{-2}\):
\[ 4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2} \]
Now, we can express \(17 \times 10^{-2}\) in standard decimal form:
\[ 17 \times 10^{-2} = 0.17 \text{ inches} \]
So, the total length of the two insects is \(0.17\) inches.