To find the total length of the two insects, we can add their lengths together.
The lengths of the insects are:
- First insect: \( 4 \times 10^{-2} \) inches
- Second insect: \( 1.3 \times 10^{-1} \) inches
First, we can rewrite both numbers with the same exponent for easier addition. We can convert \( 1.3 \times 10^{-1} \) to have the same exponent as \( 4 \times 10^{-2} \):
\[ 1.3 \times 10^{-1} = 1.3 \times 10^{-1} = 13 \times 10^{-2} \]
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 need to express \( 17 \times 10^{-2} \) in proper scientific notation. To do this, we convert \( 17 \) to \( 1.7 \) and increase the exponent by \( 1 \):
\[ 17 \times 10^{-2} = 1.7 \times 10^{-1} \]
Thus, the total length of the two insects in scientific notation, expressed to one decimal place, is:
\[ \boxed{1.7 \times 10^{-1}} \] inches.