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
Okay. Let’s say you drive from New York to San Francisco… that’s about 3000 miles, right? You get there, park your car, and it rolls back an inch. So now you went 3000 miles minus 1 inch, or 2999 miles 5279 feet and 11 inches.
That’s absurd, right? Because NY to SF isn’t exactly 3000 miles… and even if it was, it’s certainly not exact to the inch. So how can you solve this?
That’s what significant digits are for. When you give somebody a number, you give them not only the value for the number, but you also tell them how well you know the number. 3000 miles isn’t wrong, it’s just not super accurate. If instead I said 2902 miles, you can infer that I know this down to the number of miles. If I said 2902.3 miles, you can infer that I know this down to one tenth of a mile.
There are rules for adding and multiplying significant digits as well. For example, if one person borrowed your car and drove “714 miles” and somebody else drove your car and drove “I dunno… 500 miles,” you can add them up and get 1214 miles… except that is implying that you know this to the mile. Really you only know this to the nearest hundred miles, so it would be more accurate to say “1200 miles,” because you added 714 and “about 500.”
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