Question

A certain insect is approximately 4×10^−2
4
×
10
−
2
inches long. A second insect is about 1.3×10^−1
1.3
×
10
−
1
inches long. What is the total length of the two insects in inches?

Answer 1

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

1. The length of the first insect: \(4 \times 10^{-2}\) inches
2. The length of the second insect: \(1.3 \times 10^{-1}\) inches

To add these two numbers, it is helpful to express them with the same exponent.

Convert \(1.3 \times 10^{-1}\) to have the same exponent as \(4 \times 10^{-2}\):

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

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 can express \(17 \times 10^{-2}\) in standard decimal form:

\[
17 \times 10^{-2} = 0.17 \text{ inches}
\]

So, the total length of the two insects is \(0.17\) inches.