# How many significant figures?

By Marcus Wilson 07/09/2012 2

The overstating of accuracy is something that physics teachers have to continually correct. Just because one’s calculator gives an answer to ten significant figures doesn’t mean one should quote it to ten significant figures.

I’ve just looked up the location of Nakedbus’s Auckland City bus stop. It was very easy to do – drawing from Google Maps. For those who are interested, one can find the bus stop at 36.8432758738427 degrees south, 174.766430854797 degrees east. That locates it to about 100 nanometres (100 billionths of a metre)  in position. No excuse for waiting in the wrong place, then.

### 2 Responses to “How many significant figures?”

• blog says:

Surely that is too many decimal places rather than sig figs. If we rounded up to 6 sig figs but left 12 or 13 decimal places, ie 36.8433000000000 S; 174.766000000000 E. then we would be still located to about 100 nm precision, albeit less accurately. Losing all the 0s would put you within 10 m2, which is more than adequate.

• Michael Edmonds says:

Marcus, this also is a common occurrence when teaching chemistry, for example, students telling me that wine contains 5.8745643% alcohol.

blog, 36.8433000000000 still contains 15 significant figures, by including the zeros you are making them significant, as opposed to 36.8433 which has 6 sig fig’s
the advantage of using significant figures rather than decimal points is that it allows consistency in calculation when the position of the decimal point may change.