Add Numbers in Scientific Notation Practice

Question

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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)
Remaining Attempts : 3
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Answer 1

To add the lengths of the two insects in scientific notation, we need to ensure they have the same exponent before we can sum them up.

The lengths are:

• Insect 1: \( 4 \times 10^{-2} \) inches
• Insect 2: \( 1.3 \times 10^{-1} \) inches

First, we can rewrite the second insect's length to have the same exponent as the first one:

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

Now we have:

• Insect 1: \( 4 \times 10^{-2} \)
• Insect 2: \( 13 \times 10^{-2} \)

Now we can add these together:

\[ (4 + 13) \times 10^{-2} = 17 \times 10^{-2} \]

Now, we convert \( 17 \times 10^{-2} \) into proper scientific notation.

To do this, we need to move the decimal point in 17 one place to the left, which gives us:

\[ 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1} \]

Thus, the total length of the two insects in scientific notation, rounded to one decimal place, is:

\[ \mathbf{1.7 \times 10^{-1}} \text{ inches} \]