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Sig fig rules in measurements? General Chem 1st Semester?

A 10 mL graduated cylinder has calibration marks representing each mL and 0.1 mL. Accurate readings should be estimated and recorded to the nearest:

a) 1.0 mL
b) 0.1 mL
c) 0.01 mL
d) 0.001 mL

My instinct says c) 0.01 because you are supposed to have one estimated digit after the 0.1 (or are estimated digits only used in the sig fig rules for "calculations" and not for "measurements"?) My chem lab teacher just confused me more when I asked for clarification.

He said for the centigram balance scale we write to the 0.01 (which does not include an estimated digit) and for the milligram digital scale we write exactly what is shown on the screen, to the 0.001 (which also does not include an estimated digit).

So when do we include an estimated digit, and when do we not include an estimated digit?

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