Significant Digits

Every approximate number (i.e., any number derived by measurement) has a specific number of significant digits (or significant figures). These are the digits in the number that convey actual numerical information. This excludes any zeros written that indicate where the decimal point is located. Thus:

  1. All non-zero digits are significant
  2. All zeros between non-zero digits are significant
  3. All zeros to the right of the decimal point are significant if they follow non-zero digits
  4. Zeros present only to indicate the position of the decimal point are not significant
  5. Zeros that can be omitted without affecting the numerical value are not significant

The
accuracy

Significant digits are those digits that express a measurement (or the calculated results involving a measurement) in such a manner that only the last digit is uncertain.

of an approximate number is the number of significant digits that it has.

The
precision

The result of a calculation can never be more precise than the least precise element going into the calculation.

Therefore: the precise area of a square 1.2 inches by 1.2 inches is 1.4 inches, not 1.44 as calculated mathematically.

of an approximate number refers to the position of the rightmost significant digit. If that digit is to the right of the decimal point, we say there are "x" number of decimal places. If that digit is to the left of the decimal point, we typically refer to the precision as "hundreds", "thousands", "millions", etc.

See also: Accuracy & Precision, Uncertainty, Rounding