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 in inches? Use scientific notation to express your answer to 1 decimal place.(1 point)
Answers
Answered by
GPT-4o mini
To find the total length of the two insects, we need to add the lengths expressed in scientific notation:
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
First, we can rewrite \(1.3 \times 10^{-1}\) in terms of the same exponent as the first insect's length (\(10^{-2}\)):
\[
1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10^{1}}{10^{1}} = 1.3 \times \frac{10^{-1}}{10^{-2}} = 1.3 \times 10^{1} \times 10^{-2} = 13 \times 10^{-2}
\]
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 proper scientific notation:
\[
17 \times 10^{-2} = 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1}
\]
So, the total length of the two insects is:
\[
\boxed{1.7 \times 10^{-1}} \text{ inches}
\]
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
First, we can rewrite \(1.3 \times 10^{-1}\) in terms of the same exponent as the first insect's length (\(10^{-2}\)):
\[
1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10^{1}}{10^{1}} = 1.3 \times \frac{10^{-1}}{10^{-2}} = 1.3 \times 10^{1} \times 10^{-2} = 13 \times 10^{-2}
\]
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 proper scientific notation:
\[
17 \times 10^{-2} = 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1}
\]
So, the total length of the two insects is:
\[
\boxed{1.7 \times 10^{-1}} \text{ inches}
\]