Significant Digits
Rules for Determining Significant Digits
Rule #1: Digits other than zero are always significant.
96 g 2 significant digits
61.4 g 3 significant digits
0.52 g 2 significant digits
Rule #2: One or more final zeros used after the decimal point are always significant.
4.72 km 3 significant digits
4.7200 km 5 significant digits
82.0 m 3 significant digits
Rule #3: Zeros between two other significant digits are always significant.
5.029 m 4 significant digits
306 km 3 significant digits
Rule #4: Zeros used solely for spacing the decimal point are not significant. The zeros are placeholders only.
7000 g 1 significant digit
0.00783 3 significant digits
Note: If the quantity 7000 g has been measured on a balance that is accurate to the nearest gram, all four digits are significant. We must use a method to denote this. In this class a decimal will follow the number (7000.) to specify that they are all significant, or the number will be written in scientific notation. (7.000 x 103)
Not all numbers represent measurements. For instance, suppose there are 23 students in a chemistry class. How many significant digits are in 23? The 23 is not a measurement. We do not measure the number of students in a class. We count them. Students come in natural numbers. We cannot have 23.4 or 22.8 students. Since counted objects occur in exact numbers, we consider that these numbers contain an idefinite number of significant digits.