Question

A skyscraper has a mass of 2.2×105
tons. Another skyscraper in the same town has a mass of 3.7×105
tons. What is the combined mass, in tons, of the two skyscrapers? Use scientific notation to express your answer to 1 decimal place

Answer 1

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.

Answer 2

What is the sum of 6.3×103
and 2.41×104
? Use scientific notation to express your answer

Answer 3

To find the combined mass of the two skyscrapers, we simply add their masses together.

1. The mass of the first skyscraper is \(2.2 \times 10^5\) tons.
2. The mass of the second skyscraper is \(3.7 \times 10^5\) tons.

Now we can add the two masses:

\[
(2.2 \times 10^5) + (3.7 \times 10^5) = (2.2 + 3.7) \times 10^5
\]

Calculating \(2.2 + 3.7\):

\[
2.2 + 3.7 = 5.9
\]

So, the combined mass is:

\[
5.9 \times 10^5 \text{ tons}
\]

In scientific notation, to one decimal place, the combined mass of the two skyscrapers is:

\[
\boxed{5.9 \times 10^5} \text{ tons}
\]

Answer 4

To find the total length of the two insects, we need to 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.

To add these, we need to express them with the same exponent. We can convert \(1.3 \times 10^{-1}\) to a form that uses \(10^{-2}\):

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

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 can express \(17 \times 10^{-2}\) in proper scientific notation. To convert \(17 \times 10^{-2}\) into scientific notation, we can rewrite it as:

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

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

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

Answer 5

To add \(6.3 \times 10^3\) and \(2.41 \times 10^4\), we need to express them with the same exponent.

First, we can convert \(6.3 \times 10^3\) so that it has the same exponent as \(2.41 \times 10^4\):

\[
6.3 \times 10^3 = 6.3 \times 10^3 \times \frac{10}{10} = 63 \times 10^2
\]

Now we can rewrite \(2.41 \times 10^4\) in terms of \(10^3\):

\[
2.41 \times 10^4 = 2.41 \times 10^4 \times \frac{10^{-1}}{10^{-1}} = 24.1 \times 10^3
\]

Now, we have:

- \(63 \times 10^2\) can be rewritten as \(0.63 \times 10^3\)
- \(24.1 \times 10^3\)

Now we can add those two:

\[
(0.63 \times 10^3) + (24.1 \times 10^3) = (0.63 + 24.1) \times 10^3
\]

Calculating \(0.63 + 24.1\):

\[
0.63 + 24.1 = 24.73
\]

So, we have:

\[
24.73 \times 10^3
\]

Now to convert \(24.73 \times 10^3\) into standard scientific notation:

\[
24.73 = 2.473 \times 10^1
\]

Thus:

\[
24.73 \times 10^3 = 2.473 \times 10^1 \times 10^3 = 2.473 \times 10^4
\]

Finally, expressing the answer in scientific notation, we have:

\[
\boxed{2.473 \times 10^4}
\]