Significant Digits (Figures)
aka: “Sig Figs”
The precision of a number is shown by its last (rightmost) significant figure.
Unless otherwise stated, the last digit is doubtful and the correct value
is assumed to be somewhere between one less and one more than the given number.
How many significant digits (figures) does a number have?
- All non-zero digits are significant.
- All zeros between significant digits (figures) are significant.
- No zeros before the first non-zero digit are significant.
- Sometimes zeros after the last non-zero digit
are significant. It is an ALL or NONE situation.
- If ANY of the ‘trailing’ zeros follow
the decimal point then ALL of them are significant.
- If NONE of the ‘trailing’ zeros follow
the decimal point then NONE of them are significant.
How many significant digits (figures) does the result have?
- Multiplication:
- The product has the SAME NUMBER of significant digits (figures) AS the
multiplicand with the FEWEST significant digits (figures).
- Division:
- The quotient has the SAME NUMBER of significant digits (figures) AS the
divisor or dividend with the FEWEST significant digits (figures).
- Addition and Subtraction:
- The significant digits (figures) are determined by position - not by count.
- The last (rightmost) significant digit in a sum or difference is in the
same decimal position as the last significant digit in the least precise
of the original numbers.
- Note:
- All digits in numbers expressed in scientific notation are significant.
- An explicit definition of precision in terms of percent or absolute tolerance
is preferred to reliance on significant digits.
Thomas Fitzpatrick
St
Joseph's Preparatory School
Philadelphia, PA
13 August 2008