HELP!! i have a question!! In-fact 2 questions about measurement uncertainty In 149.9 ± 0.1 cm .... does 0.1 cm actually means 0.0999999999999 and we round it off to 0.1 . i think what i am saying is right but still want to confirm from some expert next question - in case of 4 units - 3 units where least count is 1 units answer will be 1 ± 2 units ? this method doesn't make sense in this case.

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You're misinterpreting the notation. The notation "149.9 +/- 0.1 cm" is not, despite appearances, the addition of two measurements. It's just a shorthand way of saying "the answer lies with some high probability between 149.8 cm and 150.0 cm." So you should not assign a measurement uncertainty to both the "149.9" and the "0.1", which it sounds like you are trying to do. The correct place at which to round the +/- bit is determined by your error analysis for the 149.9 bit, whatever it was. It is traditional to give only one digit in the +/- bit, although I suppose you could argue for different notations, depending on how the error analysis was done. In the second case, you are applying the rules of assigning measurement uncertainty mindlessly, using the sig dig rules, which you should not do. Always begin assigning measurement uncertainty by thinking about the measurement process and how error might accumulate. In the case of counting objects up to a number of 4, there are very few measurements I can imagine where it would be appropriate to assign any measurement uncertainty at all. Most such measurement will have an appropriate measurement uncertainty of zero. That is, they are what are often called "exact numbers." They have "infinite" significant digits, you might say. There are certainly cases where things you count should be assigned some measurement uncertainty. For example, if you dump a big box of marbles on the floor and try to count them by eye. If you spend 5 minutes on it and get 24,335, you might well assign a measurement uncertainty of +/- 10 marbles. But if you did it very carefully, over 2 hours, you might again assign an uncertainty of zero. Assigning measurement uncertainty is a judgment call, although there are mathematical tools that can usefully model some error processes. But mostly you use common sense.

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