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
- Atlanta to Baltimore
- Baltimore to Chicago
- 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
-
Distance from Atlanta to Baltimore: \[ 9.2735 \times 10^2 = 927.35 \text{ miles} \]
-
Distance from Baltimore to Chicago: \[ 9.7323 \times 10^2 = 973.23 \text{ miles} \]
-
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:
- \(927.35 + 973.23 = 1900.58\)
- \(1900.58 + 944.4 = 2844.98\)
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
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