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.
here is the Table
Atlanta Baltimore Boston Chicago Los Angeles Seattle Tampa Atlanta 0 9.2735×102 1.50511×103 9.444×102 3.10801×103 3.50307×103 6.7037×102 Baltimore 9.2735×102 0 5.7785×102 9.7323×102 3.72245×103 3.7441×103 1.37072×103 Boston 1.50511×103 5.7785×102 0 1.36663×103 4.16643×103 3.99708×103 1.90293×103 Chicago 9.444×102 9.7323×102 1.36663×103 0 2.79980×103 2.78657×103 1.61477×103 Los Angeles 3.10801×103 3.72245×103 4.16643×103 2.79980×103 0 1.5442×103 3.45696×103 Seattle 3.50307×103 3.7441×103 3.99708×103 2.78657×103 1.5442×103 0 4.06249×103 Tampa 6.7037×102 1.37072×103 1.90293×103 1.61477×103 3.45696×103 4.06249×103 0

5 answers

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:

  1. Starting City: Atlanta
  2. First Destination: Baltimore
  3. Second Destination: Boston
  4. 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
make it in plain language

Sure! Here’s the trip plan in simple terms:

  1. Start in Atlanta.
  2. Travel to Baltimore.
  3. Then go to Boston.
  4. Finally, return back to Atlanta.

Now, let's look at the distances:

  • From Atlanta to Baltimore: about 927.35 miles.
  • From Baltimore to Boston: about 577.85 miles.
  • From Boston back to Atlanta: about 1,505.11 miles.

Now, to find out the total distance you will travel, we add these distances together:

  1. Adding the distance from Atlanta to Baltimore and from Baltimore to Boston gives us 1,505.20 miles.
  2. Then, adding the distance from Boston back to Atlanta (1,505.11 miles) brings the total to 3,010.31 miles.

So, in total, your trip will cover:

  • 3,010.31 miles in plain terms.
  • In scientific terms, that's 3.01031 x 10³ miles.

That's the entire trip plan!

what is 8.15528 x 10^3 in decimal notation

To convert \( 8.15528 \times 10^3 \) into decimal notation, you simply move the decimal point 3 places to the right (because of the \( 10^3 \)).

Starting with:
8.15528

Moving the decimal 3 places to the right gives us:
8155.28

So, \( 8.15528 \times 10^3 \) in decimal notation is 8,155.28.