Answer: Yes, the significant digits convention was indicative of your uncertainty in the measurements.
Concept:
Significant Figures: In the measured value of a physical quantity, the number of digits about the correctness of which we are sure plus the next doubtful digit, are called Significant Figures.
There are certain values of physical quantities which are defined; like irrational numbers ∛2, √3, the speed of light ( 299792458... m/s), converted value of centimeter in to inches (2.54...), the refractive index of the glass with respect to the water ( 1.333....) etc. These values are defined but they have no limit of significant figures because we can consider the measurement up to any extent which differ from the measurement to the measurement.
Hence, the significant digits convention always gives the uncertainty in the measurements.