Why are measurements approximations?
Measurements are approximations because we are always limited by the precision of the measuring tool we are using.
For example, if you are using a ruler with centimetre and half-centimetre divisions (as you might find on a metre stick), you can only approximate the measurement to the nearest mm (0.1 cm).
If the ruler has millimetre divisions (as you might find on a ruler in your geometry set), you can approximate the measurement to a fraction of a mm (usually to the nearest 1/2 mm).
If using a micrometer, it is possible to be as precise as 0.001 mm. (1
If using a laser, it is possible to be as precise to the level of the nanometre, if not smaller.