The significant figures (also known as significant digits in American English, and often shortened to sig figs or sig digs) of a number are those digits that carry meaning contributing to its precision. This includes all digits except: All Leading zeros;
- Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at Identifying significant figures); and
- Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty. Numbers are often rounded to avoid reporting insignificant figures. For instance, if a device measures to the nearest gram and gives a reading of 12.345 kg, it would create false precision to express this measurement as 12.34500 kg. Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example to make them faster to pronounce in news broadcasts. Arithmetic precision can also be defined with reference to a fixed number of decimal places (the number of digits following the decimal point). This second definition is useful in financial and engineering applications where the number of digits in the fractional part has particular importance, but it does not follow the rules of significance arithmetic.