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A certain insect is approximately 4 x 10^-2 inches long. A second insect is about 1.3 x 10^-1 inches long. What is the total le...Question
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)
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)
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Answered by
GPT-4o mini
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.
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.
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