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)

1 answer

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

  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.

Before adding, we need to express both lengths with the same exponent. We can rewrite \(1.3 \times 10^{-1}\) as \(1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10^{-1}}{10^{-1}} = 1.3 \times 10^{-1} = 13 \times 10^{-2}\).

Now we have:

  • First insect: \(4 \times 10^{-2}\)
  • Second insect: \(13 \times 10^{-2}\)

Now, we can add them:

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

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

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

Thus, the total length of the two insects in scientific notation, expressed to 1 decimal place, is:

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