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
Baltimore 0
Boston 0
Chicago 0
Los
Angeles
3 0
Seattle 0
Tampa 0
a. 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. 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.
To plan a trip where we start at one city, travel to a second city, travel to a third city, and then return to the original city, we need to choose three cities from the given table. Let's choose Atlanta, Baltimore, and Boston as the cities for our trip.
First, we will calculate the distances between Atlanta and Baltimore, Baltimore and Boston, and Boston and Atlanta.
Distance between Atlanta and Baltimore: 3 x 10^2 miles (written in scientific notation)
Distance between Baltimore and Boston: 1 x 10^3 miles (written in scientific notation)
Distance between Boston and Atlanta: 6 x 10^2 miles (written in scientific notation)
To find the total distance traveled, we add up these distances:
(3 x 10^2) + (1 x 10^3) + (6 x 10^2) = 300 + 1000 + 600 = 1900 miles (written in decimal notation)
To write the total distance traveled in scientific notation, we can convert it by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point:
1900 miles = 1.9 x 10^3 miles (written in scientific notation)
Therefore, the total distance traveled is 1900 miles (decimal notation) or 1.9 x 10^3 miles (scientific notation).
To plan a trip where you start at one city, travel to a second city, travel to a third city, and then return to the original city, you need to choose three cities from the given options. Let's say we choose Atlanta as the starting city, followed by Baltimore, then Boston, and finally return to Atlanta.
To calculate the total distance traveled, we need to sum up the distances between each consecutive pair of cities.
1. Atlanta to Baltimore: The distance between Atlanta and Baltimore is given as 0 in the table.
2. Baltimore to Boston: The distance between Baltimore and Boston is also given as 0.
3. Boston to Atlanta: To find the distance between Boston and Atlanta, we need to scroll up or across the table until we find the cell where "Boston" is in the row header and "Atlanta" is in the column header. In this cell, we see the distance is given as 0.
Now, let's calculate the total distance traveled:
Distance from Atlanta to Baltimore: 0 miles
Distance from Baltimore to Boston: 0 miles
Distance from Boston to Atlanta: 0 miles
Total distance traveled = 0 miles in decimal notation.
In scientific notation, the total distance traveled remains the same since all distances are 0.
Therefore, the total distance traveled is 0 miles in both decimal notation and scientific notation.
To 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, we need to choose three cities from the given options.
Let's choose the cities in the following order: Atlanta, Chicago, Seattle, and finally back to Atlanta.
Using the given table, we can find the distances between these cities:
Atlanta to Chicago: 0 (already in Atlanta)
Chicago to Seattle: 0 (already in Chicago)
Seattle to Atlanta: 3
To find the total distance traveled, we add up the distances:
0 (Atlanta to Chicago) + 0 (Chicago to Seattle) + 3 (Seattle to Atlanta) = 3 miles.
So, the total distance traveled is 3 miles.
In decimal notation, the total distance traveled is also 3 miles.
In scientific notation, the total distance traveled is 3.0 x 10^0 miles.