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.
First city: 3.10801 x 10^3
Second city: 6.7037 x 10^2
Third city: 1.50511 x 10^3
returning city : 3.10801 x 10^3
To calculate the total distance traveled, we need to find the distance between each pair of cities and add them up.
Distance from first city to second city:
3.10801 x 10^3 - 6.7037 x 10^2 = 3.10801 x 10^3 - 0.67037 x 10^3
= 2.43764 x 10^3
Distance from second city to third city:
6.7037 x 10^2 - 1.50511 x 10^3 = 0.67037 x 10^3 - 1.50511 x 10^3
= -0.83474 x 10^3
Distance from third city back to first city:
1.50511 x 10^3 - 3.10801 x 10^3 = 1.50511 x 10^3 - 0.310801 x 10^4
= -1.7999 x 10^3
Total distance traveled:
(2.43764 x 10^3) + (-0.83474 x 10^3) + (-1.7999 x 10^3)
= 2.43764 x 10^3 - 0.83474 x 10^3- 1.7999 x 10^3
= 7.072 x 10^2
Therefore, the total distance traveled is 707.2 in decimal notation and 7.072 x 10^2 in scientific notation.
To calculate the total distance traveled, we need to find the sum of the distances between each city.
1. The distance between the first city (3.10801 x 10^3) and the second city (6.7037 x 10^2) is:
3.10801 x 10^3 + 6.7037 x 10^2 = (3.10801 + 0.67037) x 10^3 = 3.77838 x 10^3
2. The distance between the second city (6.7037 x 10^2) and the third city (1.50511 x 10^3) is:
6.7037 x 10^2 + 1.50511 x 10^3 = (0.67037 + 1.50511) x 10^3 = 2.17548 x 10^3
3. The distance between the third city (1.50511 x 10^3) and the returning city (3.10801 x 10^3) is:
1.50511 x 10^3 + 3.10801 x 10^3 = (1.50511 + 3.10801) x 10^3 = 4.61312 x 10^3
4. Finally, to get the total distance traveled, we add up the distances from step 1, step 2, and step 3:
3.77838 x 10^3 + 2.17548 x 10^3 + 4.61312 x 10^3 = (3.77838 + 2.17548 + 4.61312) x 10^3 = 10.56798 x 10^3
Therefore, the total distance traveled, both in decimal notation and scientific notation, is:
10.56798 x 10^3 OR 1.056798 x 10^4.
To plan the trip and calculate the total distance traveled, we need to add up the distances between each city.
First, let's list the cities in the order we're traveling:
1. First city: 3.10801 x 10^3
2. Second city: 6.7037 x 10^2
3. Third city: 1.50511 x 10^3
4. Returning to the original city: 3.10801 x 10^3
To calculate the total distance traveled, we'll add up the distances between each consecutive city.
Distance from the first city to the second city:
3.10801 x 10^3 + 6.7037 x 10^2 = 3.77838 x 10^3
Distance from the second city to the third city:
6.7037 x 10^2 + 1.50511 x 10^3 = 2.17548 x 10^3
Distance from the third city back to the first city:
1.50511 x 10^3 + 3.10801 x 10^3 = 4.61312 x 10^3
Now, we can calculate the total distance traveled by adding up the distances between each city:
Total distance traveled = 3.77838 x 10^3 + 2.17548 x 10^3 + 4.61312 x 10^3 = 10.56698 x 10^3
In decimal notation, the total distance traveled is approximately 10,566.98 units. In scientific notation, this is written as 1.056698 x 10^4.