Simply put, significant figures are numbers that actually mean what they say. It is definitely possible for numbers that have no meaning or fact to them to emerge as a result of a calculation. This is particularly true today when there are pocket calculators which will fill the whole viewing screen with numbers whether they have any meaning or not.

Suppose that the following population data is available for the City of Edmonton; the City of Ft. McMurray, 500 km to the north; and the village of Wandering River, which is halfway in between.

The total population of all three places calculates out to be 984,963 but obviously not all of the six figures have any real meaning.

The figure given for the City of Edmonton really specifies that the population is somewhere between 940 500 and 941 500. In other words, there will be a tolerance in the sum of 500 persons. In view of this, the population figure for Wandering River has no meaning at all in the sum, while the hundreds digit for Ft. McMurray is relevant, in calculating the sum, only to the extent of bumping the thousands digit from 3 to 4.

When due regard is given to the real significance of the figures, the total population of the three communities should be recorded as 985 000.

The loss of meaning, or significance, always occurs in the trailing digits.