Question

In 1867, the United States purchased Alaska from Russia. Alaska is about 5.9 × 105 square miles. The United States paid about $12.20 per square mile. Approximately how much did the United States pay Russia for Alaska?

Complete the steps to answer the question.

1. Write the expression:       (5.9 × 105)(12.2)

2. Multiply the decimal values:     
× 105

3. Write in scientific notation:     
×

The United States paid Russia approximately
for Alaska.

Answer 1

Let's solve each step as outlined:

1. **Write the expression**:
\[
(5.9 \times 10^5)(12.2)
\]

2. **Multiply the decimal values**:
First, multiply \(5.9\) and \(12.2\):
\[
5.9 \times 12.2 = 71.98
\]
Now, we also have \(10^5\) from \(5.9 \times 10^5\):
- So the expression becomes:
\[
71.98 \times 10^5
\]

3. **Write in scientific notation**:
We want to express \(71.98\) as \(7.198 \times 10^1\) (since \(71.98 = 7.198 \times 10^1\)). So, we can rewrite:
\[
71.98 \times 10^5 = 7.198 \times 10^1 \times 10^5
\]
By combining the powers of 10:
\[
7.198 \times 10^{1+5} = 7.198 \times 10^6
\]

Therefore, the United States paid Russia approximately:
\[
\text{The United States paid Russia approximately } 7.198 \times 10^6 \text{ dollars for Alaska.}
\]

In standard form, this is approximately **$7,198,000**.