Resolving Conflicts in Different Values of Unceratinty

Problem: I make several measurements on the mass of an object. The balance has an ILE of 0.02 grams. The average mass is 12.14286 grams, the average deviation is 0.07313 grams. What is the correct way to write the mass of the object including its uncertainty? What is the mistake in each one that is incorrect? Go to entire or click on a choice.
1. 12.14286 g Way wrong! You need the uncertainty reported with the answer. Also the answer has not been properly rounded off.
2. (12.14 ± 0.02) g Way wrong! You could not read my writing perhaps. The uncertainty is 0.07 grams. Otherwise the format of the answer is fine.
3. 12.14286 g ± 0.07313 Way wrong! You need to round off the uncertainty and the answer. Also the answer should be presented within parentheses.
4. 12.143 ± 0.073 g Almost there. Put parentheses around the numbers and it would be OK. Rounding off one more place is better.
5. (12.143 ± 0.073) g This is fine. Slightly better would be to round off one more place.
6. (12.14 ± 0.07) Almost there, but what pray tell are the units?
7. (12.1 ± 0.1) g Wrong. You went overboard in rounding. Stop when the uncertainty is 0.07, one significant figure.
8. 12.14 g ± 0.07 g Almost right. The answer and uncertainty should be in parentheses with unit outside.
9. (12.14 ± 0.07) g Correct!

The object has a mass of (12.14 g ± 0.07) g. This is the most correct.

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Problem:  I measure a length with a meter stick with a least count of 1 mm. I measure the length 5 times with results in mm of 123, 123, 123, 123, 123. What is the average length and the uncertainty in length?

Length, L (mm)
123 0.0 0.0
123 0.0 0.0
123 0.0 0.0
123 0.0 0.0
123 0.0 0.0
Sum 616 Sum    0.0 Sum    0.0
Average    123 Average   0.0 St. Dev.   0.0

Here the average deviation and the standard deviation are smaller than the ILE of 0.5 mm. Hence I use 0.5 mm as the unceratinty.

The object has a length of (123.0 +/- 0.5) mm.

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