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
Significant figures are those that matter. When you drive a car the actual speed is not being displayed on the speedometer. Something close to it is. If you are driving at 35.45 mph. Your car will only display two digits (or three is you are going faster than 99 mph.)
The displayed speed has two significant figures.
The limit on significant figures reported is the least accurate measurement used. Imagine that your car gets 22.35 mpg. But you have a havd gas can that hold 5 gallons.
Saying that you are able to travel 5*22.35 =111.75 miles is kind of silly. The 5 gallon tank might have had more or less gasoline that 5 gallons. So we would only report one significant figure and we would say we can go 100 miles. The zeros to the right of the 1 are not significant, they are place holders to give you magnitude.
If you had been asked what is the average millage per gallon of your car, you might have reported two significant figures 22.35 you look at the 5 so you rough up the 0.35 to 0.4 you then round again 0.4 rounds down to zero. So 22.35 mpg is reported as 22 mpg.
Going back to the 5 gallon tank. The 5 gallons is really more like 5.49-4.50 gallons because of significant figures. Those values would be rounded to 5. Writing 5.0 makes it look more precise but it is not correct since the gas can is not that accurate.
Good for you admitting that you need help.
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