Scientific Notation Portfolio

Question

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
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
3.72245 × 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

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.

Starting City: _____________ Second City: _____________ Third City: _____________

Distance between starting city and second city: _____________

Distance between second city and third city: _____________

Distance between third city and original city: _____________

Total Distance Traveled in Decimal Notation:__________________________________

Total Distance Traveled in Scientific Notation:__________________________________
Sita lives in Los Angeles, and her grandmother lives in Seattle. Sita plans to visit her grandmother three times in the next year. What is the total distance she will travel to make these three trips? Write and evaluate an expression that uses multiplication to calculate the total distance traveled. Give your answer in both decimal notation and scientific notation.

Distance from Los Angeles to Seattle: _____________

Distance from Seattle back to Los Angeles: _____________

Total Distance of one trip to Seattle and back: _____________

Total Distance of three trips (use multiplication): _____________

Total Distance of Three Trips in Decimal Notation:__________________________________

Total Distance of Three Trips in Scientific Notation:__________________________________

Using the table of distances, you are driving from Tampa to Boston and then to Chicago and your car breaks down halfway through the trip. How far did you go before stopping? Write your total distance to travel and then write the halfway distance in both decimal notation and scientific notation.

Distance fromTampa to Boston: _____________

Distance from Boston to Chicago: _____________

Total Distance if you made it all the way: _____________

Distance halfway in Decimal Notation:__________________________________

Distance halfway in Scientific Notation:__________________________________

Answer 1

Let's fill out the necessary calculations step by step:

Trip Planning

Starting City: Atlanta
Second City: Chicago
Third City: Los Angeles

Calculating Distances:

1. Distance between Atlanta and Chicago:

   • From the table: \( 9.444 \times 10^2 \) miles
   • In decimal notation: \( 944.4 \) miles

2. Distance between Chicago and Los Angeles:

   • From the table: \( 2.79980 \times 10^3 \) miles
   • In decimal notation: \( 2799.80 \) miles

3. Distance between Los Angeles and Atlanta:

   • From the table: \( 3.10801 \times 10^3 \) miles
   • In decimal notation: \( 3108.01 \) miles

Total Distance Calculated:

• Total Distance = Distance(A to C) + Distance(C to L) + Distance(L to A)
• Total Distance = \( 944.4 + 2799.80 + 3108.01 \)
• Total Distance = \( 944.4 + 2799.80 + 3108.01 = 6852.21 \) miles

Total Distance Travelled:

• Total Distance Traveled in Decimal Notation: 6852.21 miles
• Total Distance Traveled in Scientific Notation: \( 6.85221 \times 10^3 \) miles

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Sita's Trips to Seattle

1. Distance from Los Angeles to Seattle:

   • From the table: \( 3.50307 \times 10^3 \) miles
   • In decimal notation: \( 3503.07 \) miles

2. Distance from Seattle back to Los Angeles:

   • The distance is the same: \( 3.50307 \times 10^3 \) miles
   • In decimal notation: \( 3503.07 \) miles

3. Total Distance of One Trip to Seattle and Back:

   • Total Distance = Distance(LA to Seattle) + Distance(Seattle to LA)
   • Total Distance = \( 3503.07 + 3503.07 = 7006.14 \) miles

4. Total Distance of Three Trips (use multiplication):

   • Total Distance = \( 7006.14 \times 3 \)
   • Total Distance = \( 21018.42 \) miles

Total Distances for Sita:

• Total Distance of Three Trips in Decimal Notation: 21018.42 miles
• Total Distance of Three Trips in Scientific Notation: \( 2.101842 \times 10^4 \) miles

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Trip from Tampa to Boston and Chicago

1. Distance from Tampa to Boston:

   • From the table: \( 1.90293 \times 10^3 \) miles
   • In decimal notation: \( 1902.93 \) miles

2. Distance from Boston to Chicago:

   • From the table: \( 1.36663 \times 10^3 \) miles
   • In decimal notation: \( 1366.63 \) miles

3. Total Distance if you made it all the way:

   • Total Distance = Distance(Tampa to Boston) + Distance(Boston to Chicago)
   • Total Distance = \( 1902.93 + 1366.63 = 3269.56 \) miles

Halfway Distance:

• Distance halfway:
  • Halfway distance = Total Distance / 2
  • Halfway distance = \( 3269.56 / 2 = 1634.78 \) miles

Halfway Distance in Scientific Notation:

• Halfway Distance = \( 1.63478 \times 10^3 \) miles

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Summary of Results

• Trip Planning (Atlanta → Chicago → Los Angeles → Atlanta):

  • Total Distance Traveled in Decimal Notation: 6852.21 miles
  • Total Distance Traveled in Scientific Notation: \( 6.85221 \times 10^3 \) miles

• Sita's Total Distance of Three Trips:

  • Total Distance of Three Trips in Decimal Notation: 21018.42 miles
  • Total Distance of Three Trips in Scientific Notation: \( 2.101842 \times 10^4 \) miles

• Trip Breakdown (Tampa → Boston → Chicago):

  • Total Distance if you made it all the way: 3269.56 miles
  • Distance halfway in Decimal Notation: 1634.78 miles
  • Distance halfway in Scientific Notation: \( 1.63478 \times 10^3 \) miles