In a triathlon race, an athlete swam 1.5 km, cycled 40 km, and ran 15 km. Which of the alternatives below presents the order of magnitude of the distance covered by the athlete in meters?

An athlete is training for a marathon and covers a distance of 420 meters in 1 minute. Considering that the athlete maintains a constant speed, estimate the order of magnitude of the number of steps he takes when covering this distance, assuming that the average length of a step is approximately 1 meter.

The circular particle accelerator LHC, located on the border between Switzerland and France, will generate approximately 600 million proton collisions per second starting in 2009. Of these collisions, only 0.000017% will be of scientific interest. It can be concluded that the order of magnitude of the number of scientifically relevant collisions per second will be:

To solve this question, we will follow these steps: 1. First, we need to understand what the order of magnitude means. The order of magnitude is a way to classify numbers based on powers of 10. For example, if a number is between 1 and 10, its order of magnitude is 

; if it is between 10 and 100, its order of magnitude is 

, and so on. 2. Now, let's calculate the number of scientifically relevant collisions per second. To do this, we multiply the total number of collisions per second by the percentage of scientifically relevant collisions: Number of scientifically relevant collisions per second = (Total number of collisions per second) * (Percentage of scientific interest / 100) 3. We substitute the values provided in the question: Number of scientifically relevant collisions per second = (600 million collisions per second) * (0.000017% / 100) 4. Converting 600 million to scientific notation, we have: 600 million = 6 * 10^8 5. Converting the percentage to decimal form: 0.000017% = 0.000017 / 100 = 0.00000017 6. Now, we multiply the two values: Number of scientifically relevant collisions per second = (6 * 10^8) * (0.00000017) 7. Performing the multiplication: Number of scientifically relevant collisions per second = 1.02 * 10^2 8. We observe that the result, 1.02 * 10^2, is between 10 and 100. Therefore, the order of magnitude is 

In an experiment in the field of astronomy, an astronomer calculates the distance between Earth and a natural satellite of a planet in our solar system. He uses the order of magnitude to facilitate the understanding of his data and interaction with his colleagues. The calculated distance is approximately 9,461 × km. (a) Determine the order of magnitude of this distance. (b) Suppose the distance between Earth and another satellite is 3.05 × km. In comparative terms, what is the order of magnitude of the difference in distances between the two satellites? (c) If the speed of light is approximately 3.0 × km/s, what is the order of magnitude of the time it takes for light to travel the distance between Earth and the first satellite?

When analyzing the circumference of the Earth, which is approximately 40,000 km, we can compare it to the circumference of a soccer ball, which is about 0.8 m. Estimate the ratio between the order of magnitude of the Earth's circumference and the circumference of the soccer ball.

Question bank: Order of Magnitude

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