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When measuring, you should always report data to the first uncertain digit.
For example, let's say that I have a block that I will measure with a 12-inch ruler which only has the numbers 1 through 12 on it and no other hash marks.
The edge of my block lands between the 7 and 8. Now I know for sure that my block is at least 7 inches long. What I need to do now is give my best guess as to how much beyond 7 it really is. You can mentally divide the space between the 7 and 8 into 10 equal parts. Maybe it looks like it is a little more than half the distance to the 8 so I might report it as 7.6 inches. Thing is your eyes are different than mine and you might think it is 7.7 which is why we cannot say 7.65 because the tenths place is uncertain.
Of course this is where the idea of significant figures comes in. All of this uncertainty in our measurements.
So, that is how the last digit is determined. It is based on the first uncertain digit.
This is very much a nutshell as far as significant figures go so if you need anything else just ask! |