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!
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.