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Once upon a time, back before the 1970's, almost all scientificFrom: http://www.digipac.ca/chemical/sigfigs/contents.htm
calculations were done by using a slide rule. A slide rule could
only display three significant digits, sometimes, rarely four. So
all calculations were automatically rounded off to three significant
digits. The invention of the electronic calculator changed all that.
Calculators can easily display many – perhaps eight to ten –
significant digits. Realistically though, it would be extremely rare
to have data that justifies that many digits in the answer.
So, its largely the calculator that is responsible for the emphasis
on significant digits in science classes.