# 7.04 Consistency between significant digits and uncertainty

We have previously discussed that we can express the precision in the measurement either by explicitly by stating the uncertainty or implicitly by the number of significant figures we use. e.g.
explicit: 12.0 +/- 0.2 mm means the uncertainty interval is from 11.8 to 12.2 mm
implicit: 2.5mm means the uncertainty interval is from 2.45 to 2.55mm

When expressing the uncertainty explicitly there must be consistency between the number of significant figures used to express the nominal value and the number of significant figures used for the uncertainty.

Consider the following.
A measurement has been made of the diameter of a metal rod and the value recorded is. 12 +/- 0.01cm

In this example the number of digits used to express the first part of the measurement is not consistent with the uncertainty.

Recording the first part of the measurement as 12 cm implies that the measuring instrument only had a resolution of 1cm (which is why the value is only recorded to the nearest centimetre ie 12 cm). However if this was the case then it would not have been possible to determine the uncertainty interval to be within +/- 0.01cm. (i.e. not possible with an instrument that only had centimetre markings!)

Alternatively if the resolution of the instrument was 0.01cm this would have enabled the uncertainty to be determined to within 0.01cm. However if this was the case the instrument would also have been able to determine the first part of the measurement value to the same resolution e.g 12.27cm or 12.32 cm etc.

Therefore in the above example the value should have been written as 12.00 +/- 0.01cm