# 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