A certain insect is approximately 4×10−2

Question

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)

Answer 1

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

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.

First, we need to express both lengths with the same exponent:

Convert \( 1.3 \times 10^{-1} \) to a similar exponent as \( 4 \times 10^{-2} \): \[ 1.3 \times 10^{-1} = 1.3 \times 10^{-1} = 13 \times 10^{-2} \]

Now we can add the two lengths: \[ 4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2} \]

Next, we convert \( 17 \times 10^{-2} \) to scientific notation: \[ 17 \times 10^{-2} = 1.7 \times 10^{-1} \]

Thus, the total length of the two insects in scientific notation to 1 decimal place is: \[ \boxed{1.7 \times 10^{-1}} \text{ inches} \]