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

1 answer

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.