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)

Answer 1

What is the sum of 6.3×103
and 2.41×104
? Use scientific notation to express your answer.(1 point)

Answer 2

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

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

Before we can add the two lengths, we should express them with the same exponent. The second insect’s length is in \( 10^{-1} \) notation, so we can convert the first insect’s length into this format:

\[
4 \times 10^{-2} = 0.4 \times 10^{-1}
\]

Now both insects can be expressed as:

1. First insect: \( 0.4 \times 10^{-1} \)
2. Second insect: \( 1.3 \times 10^{-1} \)

Now we can add these lengths together:

\[
0.4 \times 10^{-1} + 1.3 \times 10^{-1} = (0.4 + 1.3) \times 10^{-1} = 1.7 \times 10^{-1}
\]

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

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

Answer 3

To find the sum of \(6.3 \times 10^3\) and \(2.41 \times 10^4\), we need to express both numbers with the same power of 10.

The first number, \(6.3 \times 10^3\), can be rewritten to match the exponent of the second number, \(10^4\):

\[
6.3 \times 10^3 = 0.63 \times 10^4
\]

Now we can add the two numbers:

\[
0.63 \times 10^4 + 2.41 \times 10^4 = (0.63 + 2.41) \times 10^4 = 3.04 \times 10^4
\]

Therefore, the sum of \(6.3 \times 10^3\) and \(2.41 \times 10^4\) in scientific notation is:

\[
\boxed{3.04 \times 10^4}
\]