I've seen conflicting statements on whether the implied uncertainty of a measurement should be interpreted to be ±½ or ±1 of its least significant figure. Wikipedia goes with the ±½ convention:
Applying 10½ meters in a scientific or engineering application, it could be written 10.5 m or 10.50 m, by convention meaning accurate to within one tenth of a meter, or one hundredth. The precision is symmetric around the last digit. In this case it's half a tenth up and half a tenth down, so 10.5 means between 10.45 and 10.55. Thus it is understood that 10.5 means 10.5±0.05, and 10.50 means 10.50±0.005.
However, this definition feels unintuitive, since it allows for no overlap between implied ranges, making it impossible to confidently express measurements whose perceived value lies midway between two units. For example, suppose that I have a ruler with millimeter marks. I measure an object whose length appears to be midway between the 77 mm and 78 mm marks. If the implied uncertainty is ±1, then I could give the measured length as either 77 mm or 78 mm, since both implied ranges would be correct (76–78 mm and 77–79 mm respectively). However, if the implied uncertainty is ±½, then it becomes impossible for me to express the measured length with confidence. If I give it as 78 mm, then my implied range would be 77.5–78.5 mm, making my measurement wrong if the object is actually 77.4999 mm – yet I have no way of detecting this 0.0001 mm discrepancy.
Given the above, why do sources promote the ±½ convention? Are they suggesting that it's acceptable for a measurement to have a confidence level as low as 50% for these midway values, or am I missing something?
Edit: I agree with the feedback that it's better to express the uncertainty explicitly in scientific contexts where it matters. However, I'm more interested in the everyday interpretation of expressed measurements, where significant figures are only intended to convey a rough indication of precision. My argument is that, even in these situations, the ±½ convention is fundamentally flawed, since it results in confidence levels as low as 50%, and any sources that promote it would be better off switching to the ±1 convention.