I’m ashamed to be a senior majoring in math and I still haven’t grasped the concept of amusing significant digits! I seriously need it explained to me like I’m a child.
In: Mathematics
How long does it talk you to walk to class?
If you said 10 minutes, I’d assume you were just rounding to a convenient number, and the actual time might be anywhere from 8 to 12 minutes. But if you said 11 minutes, that shows you know the duration to a higher degree of accuracy, otherwise you would have said 10. I know that it takes you 11 minutes, not 10, not 12.
That’s essentially what significant figures are. All measurements have a degree of inaccuracy, and significant figures are kind of like a guarantee, if you say 174 rather than 200 or 174.2841230, I know you mean 174 +/- 0.5 and can make assumptions based on that degree of accuracy.
One mistake students often make is overstating accuracy by using to many significant figures. Just because your calculator gives you 10 decimal places, that doesn’t mean your answer has that degree of accuracy. You need to analyze and round to the appropriate number of significant figures. Also, when you multiply two numbers together, your answer has as many significant figures as the least accurate number. If you traveled 56.7754 km in “about” 2 hours, your speed is 30 km/h. It doesn’t matter how accurately you measured the distance, if you only know the time to one significant figure, you only know the answer to one significant figure.
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