Let's plan a trip starting in Atlanta and visiting Baltimore and then Boston before returning to Atlanta.
Here are the details of the trip:
- Starting City: Atlanta
- First Destination: Baltimore
- Second Destination: Boston
- Returning to: Atlanta
Next, we retrieve the distances from the table:
- Distance from Atlanta to Baltimore: \( 9.2735 \times 10^{2} \) miles
- Distance from Baltimore to Boston: \( 5.7785 \times 10^{2} \) miles
- Distance from Boston back to Atlanta: \( 1.50511 \times 10^{3} \) miles
Now, let's calculate the total distance traveled:
\[ \text{Total Distance} = \text{Distance (Atlanta to Baltimore)} + \text{Distance (Baltimore to Boston)} + \text{Distance (Boston to Atlanta)} \]
Substituting the respective distances:
\[ \text{Total Distance} = 9.2735 \times 10^{2} + 5.7785 \times 10^{2} + 1.50511 \times 10^{3} \]
Now, we can convert everything to the same format (either standard notation or scientific notation) for easy addition. The distances are:
- \( 9.2735 \times 10^{2} = 927.35 \)
- \( 5.7785 \times 10^{2} = 577.85 \)
- \( 1.50511 \times 10^{3} = 1505.11 \)
Adding them:
\[ \text{Total Distance} = 927.35 + 577.85 + 1505.11 \]
Calculating:
\[ 927.35 + 577.85 = 1505.20 \] \[ 1505.20 + 1505.11 = 3010.31 \]
So, the total distance traveled is:
\[ \text{Total Distance} = 3010.31 \text{ miles} \]
Now, converting this into scientific notation:
\[ 3010.31 = 3.01031 \times 10^{3} \]
Summary of the Trip:
- Cities Visited: Atlanta → Baltimore → Boston → Atlanta
- Total Distance Traveled:
- In decimal notation: 3010.31 miles
- In scientific notation: 3.01031 x 10³ miles