Hello, I have some questions on uncertainties in measurement: Say you have a ruler with 1mm graduations, and you are trying to measure the length of a metal rod. One end of the metal rod is at the 120.0mm graduation, and the other is in between the 19 and 20mm graduation, and you approximate its value to be 19.5mm. The uncertainty in these two measurements is half the smallest scale division, and therefore +-0.5mm. The length of the metal rod = 120.00mm - 19.5mm = 100.5mm The uncertainty in the length = 0.5mm + 0.5mm = 1mm However, since the uncertainty in the length is 1mm, would we have to round the length of the metal rod up to 101mm since stating the length of the metal rod as 100.5mm would create false precision? (My textbook states that the length would remain unrounded as 100.5mm +- 1.00mm but I fail to see the reasoning behind it.) If it does create false precision, then my second question would be: Would uncertainties such as +- 0.14m, or +-0.32m, or +-0.54m, be contradictory in nature, since they are creating false precision? For example, wouldn't an uncertainty of +-0.14m be contradictory in nature, since it implies a precision of 0.01m, when the measurement, as stated by the uncertainty, is only precise to +-0.14m? Shouldn't an uncertainty of +-0.14m always be rounded upwards to +-0.2m, and all uncertainties in general be rounded to 1sf to avoid false precision? I know these questions are quite rudimentary but I can't seem to figure them out -- thank you for all your help!