To find the total length of the two insects, we need to add their lengths together, which are given in scientific notation:
- The length of the first insect is \(4 \times 10^{-2}\) inches.
- 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:
\[ \boxed{1.7 \times 10^{-1}} \text{ inches.} \]
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