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 3.7441×103 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

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 3.7441×103 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
Sita lives in Los Angeles, and her grandmother lives in Seattle. Sita plans to visit her grandmother three times in the next year. Assuming she travels the direct straight-line distance between the cities on each trip, 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.

GPT-4o mini · Answer

To determine the total distance Sita will travel between Los Angeles and Seattle, we first need to find the distance between these two cities from the table provided.

The distance from Los Angeles to Seattle is given as: \[ 1.5442 \times 10^3 \text{ miles} \]

This is equivalent to: \[ 1.5442 \times 10^3 = 1544.2 \text{ miles} \]

Since Sita plans to make this trip three times, we can represent the total distance traveled using a multiplication expression: \[ \text{Total distance} = 3 \times (1.5442 \times 10^3) \]

Now, multiplying the distance by 3: \[ 3 \times 1.5442 \times 10^3 = 4.6326 \times 10^3 \]

Now, we can also convert \( 4.6326 \times 10^3 \) back into decimal notation for the total distance: \[ 4.6326 \times 10^3 = 4632.6 \text{ miles} \]

Thus, the total distance Sita will travel for her three trips is:

In decimal notation: 4632.6 miles
In scientific notation: \( 4.6326 \times 10^3 \) miles