Question

a certain insect is approximately 4×10 with power of -2 inches long a second insect is about 1.3×10 negative one power 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:

1. First insect's length: \( 4 \times 10^{-2} \) inches
2. Second insect's length: \( 1.3 \times 10^{-1} \) inches

Before adding them, we should express both lengths in the same power of ten. The second insect is in \( 10^{-1} \) notation, which is larger than \( 10^{-2} \). Therefore, we can convert the first insect's length to match the second insect's power of ten:

\[
4 \times 10^{-2} = 0.04 \times 10^{-1}
\]

Now we can add the two lengths together:

\[
0.04 \times 10^{-1} + 1.3 \times 10^{-1} = (0.04 + 1.3) \times 10^{-1}
\]

Calculating \( 0.04 + 1.3 \):

\[
0.04 + 1.3 = 1.34
\]

Now, we write it in scientific notation:

\[
1.34 \times 10^{-1}
\]

Finally, since you requested the answer to one decimal place, we round \( 1.34 \) to one decimal place:

\[
\mathbf{1.3 \times 10^{-1}}
\]

Thus, the total length of the two insects is \( \mathbf{1.3 \times 10^{-1}} \) inches.