First of all, I am still not sure what a significant figure is. Some places have told me it is a digit that doesn't change over repeated measurements, others say it's just the number of digits you report in a measurement, then the fractional uncertainty says how many sig figs you should have but the absolute uncertainty almost always changes digits that are "significant".

a.)How far can you guess the measurement? If my ruler only goes to 1mm and I measure something between 1.1 and 1.2cm can I guess a smaller digit?

b.)In general do you estimate past the smallest division on an instrument? Is the absolute uncertainty half of that? How does uncertainty as a standard deviation come in from here? How do you know how many sig figs to keep in the standard deviation?

c.)How does the fractional uncertainty relate to the number of significant figures in a measurement? How does it relate to the size of the round off error? For example you have a measurement of 1.00 which the rules say has 3 sf. It has an uncertainty of 0.05. The fractional uncertainty of this is 5% which says it should only have 2sf. The range of this measurement would be [0.95 1.05] which changes all of the digits in the measurement, so are any of them are actually "significant"?