Question

a certain insect is approximately 4×10 to the power of -2 inches long a second insect is about 1.3×10 to the power of -1 inches long what is the total length of the two insects and inches use scientific notation to express your answer to one decimal place

Answer 1

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

1st insect: \(4 \times 10^{-2}\) inches
2nd insect: \(1.3 \times 10^{-1}\) inches

First, we can express both numbers in a comparable format. We can rewrite \(1.3 \times 10^{-1}\) in terms of \(10^{-2}\):

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

Now we can add the two lengths together:

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

Next, we need to convert \(17 \times 10^{-2}\) into proper scientific notation, which requires the coefficient to be between 1 and 10:

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

So the total length of the two insects in scientific notation is:

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