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Orders of magnitude?


alexalexalex

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Quick tips before I answer your question
1) "I'm confused" is not the best way to ask question. You should at least identify the place where you know everything up to it, and becomes lost afterwards.
2) "Exactly what you need to know" is not the way to approach your pretty tough courseload. IB is relatively different from ICGSE and not all questions will be as straightforward as before. Now it's fine since it's just Topic 1 but for later topics, you often have to use ideas across multiple topics to solve a single problem. 

Take an example from comparing orders of magnitude: the diameter of Earth is 1.27 × 104 km, the Earth-Moon distance is 3.84 × 105 km, you should able to tell that the Moon is about 30 times further to you than the opposite side on Earth just at a glance, without using a calculator.

The Sun, for example has a radius of 6.96 × 105 km. So without a calculator, you should see that the solar radius is about 100 times than that of Earth, so the sun has about 10 000 times the surface area and 1 000 000 times the volume as Earth. (Because 2-dimensional values are proportional to factors of radius-squared, and for 3-dimensional values, it's radius-cubed). 

Finally, the speed of light is 3.00 × 108 m/s, and the Sun is 1.50 × 108 km away so how long would it take for Sun's light to reach the Earth? We can first reconcile the units and say the speed of light is 3.00 × 105 km/s, so distance/speed is roughly 0.5 * 103 or 5 × 10seconds or 500 seconds. 60 seconds to a minute, and 540 seconds would be 9 minutes. So it takes about 8.something or under 9 minutes. Eventually you should be quite comfortable with doing these in your head. These are relatively friendly numbers but later in the course you may need to answer questions of non-whole-number exponents and numbers not as nice as 1.50 ÷ 3.00. 

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