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The top speed of a Rocket Sled is 18,306 kilometers per hour. Is this faster or slower than the Autonomous Drone?

For full credit:
1) In full sentences, describe the steps you took to convert the Rocket Sled's speed into scientific notation.
2) You must include the correct Scientific Notation for the Rocket Sled to earn full points.
3) Compare the speed to the Autonomous Drone. Explain how you know it is faster or slower.

3 answers

To determine whether the Rocket Sled's top speed of 18,306 kilometers per hour is faster or slower than the Autonomous Drone, I first needed to convert the speed of the Rocket Sled into scientific notation. Here are the steps I took:

  1. I started with the number 18,306. To convert this into scientific notation, I need to express it in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
  2. I shifted the decimal point in 18,306 to the left until I got a number between 1 and 10. I moved the decimal point 4 places to the left, changing 18,306 into 1.8306.
  3. Since I moved the decimal point 4 places to the left, I have to denote that movement with a power of 10. Therefore, I write this as \( 1.8306 \times 10^4 \).
  4. As a result, the scientific notation for the Rocket Sled's speed is \( 1.8306 \times 10^4 \) kilometers per hour.

Next, I need to compare this speed to that of an Autonomous Drone. For instance, if we say that the Autonomous Drone has a top speed of 100 kilometers per hour. In scientific notation, 100 is expressed as \( 1.0 \times 10^2 \).

When I compare \( 1.8306 \times 10^4 \) (Rocket Sled) to \( 1.0 \times 10^2 \) (Autonomous Drone), I observe that the power of 10 for the Rocket Sled (\( 10^4 \)) is much larger than that of the Autonomous Drone (\( 10^2 \)). This means that \( 1.8306 \times 10^4 \) is significantly larger than \( 1.0 \times 10^2 \).

Thus, I conclude that the Rocket Sled is significantly faster than the Autonomous Drone.

write in 3 sentences

To convert the Rocket Sled's speed of 18,306 kilometers per hour into scientific notation, I moved the decimal point 4 places to the left, resulting in the number 1.8306. This is expressed as \( 1.8306 \times 10^4 \) kilometers per hour. When comparing this to an Autonomous Drone, which might have a speed of 100 kilometers per hour (or \( 1.0 \times 10^2 \)), it is clear that the Rocket Sled, at \( 1.8306 \times 10^4 \), is far faster.