The following table shows distances in miles between some cities in the United States. The distances have been written in scientific notation. 

Atlanta  Baltimore  Boston  Chicago Los Angeles  Seattle Tampa
Atlanta 0
9.2735×102

1.50511×103

9.444×102

3.10801×103

3.50307×103

6.7037×102

Baltimore
9.2735×102

0
5.7785×102

9.7323×102

3.72245×103

3.7441×103

1.37072×103

Boston
1.50511×103

5.7785×102

0
1.36663×103

4.16643×103

3.99708×103

1.90293×103

Chicago
9.444×102

9.7323×102

1.36663×103

0
2.79980×103

2.78657×103

1.61477×103

Los Angeles 
3.10801×103

3.72245×103

4.16643×103

2.79980×103

0
1.5442×103

3.45696×103

Seattle
3.50307×103

3.7441×103

3.99708×103

2.78657×103

1.5442×103

0
4.06249×103

Tampa
6.7037×102

1.37072×103

1.90293×103

1.61477×103

3.45696×103

4.06249×103

0

Plan a trip where you will start at one city, travel to a second city, travel to a third city, and then return to the original city. Assuming you could travel the direct straight-line distance between each pair of cities, how far will you travel all together? Write your total distance traveled in both decimal notation and scientific notation. Show all your work so it is clear what cities you are going to and in what order. 

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
15 days ago

Let’s plan a trip starting from Atlanta, traveling to Baltimore, then to Chicago, and finally returning to Atlanta. We will calculate the distances between each leg of the trip using the distances provided in the table.

### Trip Route
1. **Atlanta to Baltimore**
2. **Baltimore to Chicago**
3. **Chicago to Atlanta**

### Distances
From the table:
- **Atlanta to Baltimore**: \(9.2735 \times 10^2\) miles
- **Baltimore to Chicago**: \(9.7323 \times 10^2\) miles
- **Chicago to Atlanta**: \(9.444 \times 10^2\) miles

### Step-by-step Calculation
1. **Distance from Atlanta to Baltimore**:
\[
9.2735 \times 10^2 = 927.35 \text{ miles}
\]

2. **Distance from Baltimore to Chicago**:
\[
9.7323 \times 10^2 = 973.23 \text{ miles}
\]

3. **Distance from Chicago to Atlanta**:
\[
9.444 \times 10^2 = 944.4 \text{ miles}
\]

### Total Distance Calculation
Now we will sum the distances calculated:
\[
\text{Total Distance} = \text{Distance from Atlanta to Baltimore} + \text{Distance from Baltimore to Chicago} + \text{Distance from Chicago to Atlanta}
\]
\[
= 927.35 + 973.23 + 944.4
\]

Calculating the sum step-by-step:
1. \(927.35 + 973.23 = 1900.58\)
2. \(1900.58 + 944.4 = 2844.98\)

### Total Distance in Decimal Notation
\[
\text{Total Distance} = 2844.98 \text{ miles}
\]

### Total Distance in Scientific Notation
To express \(2844.98\) in scientific notation:
\[
2844.98 = 2.84498 \times 10^3
\]

### Summary
The total distance traveled during the trip starting from Atlanta, traveling to Baltimore, then to Chicago, and returning to Atlanta is:

- **Total Distance in decimal notation**: \(2844.98\) miles
- **Total Distance in scientific notation**: \(2.84498 \times 10^3\) miles