AKA: Sig Figs
During the experimental process scientists collect large
amounts of data and most of this data comes from measurements
and calculations. Therefore, a system is needed to show the
precision of their data and calculations.
The rules for significant figures is that
By using significant figures and following a few simple
rules a scientist can include the precision of the tools used
and then maintain the integrity of the data while doing
There are two types of quantities in data
- Exact numbers - result from
counting objects or from defined values like 2.54 cm = 1
- Measured numbers - are inexact
numbers and required a judgement call to determine.
Measured numbers should reflect all the certain
digits plus the first uncertain digit. If a
tool is graduated by tenths then the digits in the measurement
need to show all the digits to the tenths place (±0.1) plus one
uncertain digit (±0.01). Therefore, the precision of this tool
is ±0.01 units.
The uncertain digit is a judgement call made by the person
taking the measure-ment. All the digits before that would be
certain digits because they can actually be determined by the
tool being used.
A meter stick divided into millimeters will have a precision
of ±0.0001 meter. All of the digits up to and including the ten
thousandths place are considered significant. So, any
measurements made with this meter stick should reflect this
But, not all measurements will have the same precision
because of the different tools used in the experimental
process. So, if there is a variety of data that will be used in
calculations the results must be limited to the least precise
Significant Figure Rules
Recognizing Significant Figures (sig figs)
- All non-zero digits are significant. (1, 2, 3, 4, 5, 6,
7, 8, 9)
- All zeroes between significant figures are significant.
- Leading zeroes are never significant.
- Trailing zeroes are significant only if after a decimal
point and following a significant figure.
- Trailing zeroes between significant figures and a
decimal point are significant figures.
225 has 3 significant figures
10,004 has 5 significant
figures (Rule #2)
0.0025 has 2 significant
figures (Rule #3)
0.002500 has 4 significant
figures (Rule #4)
3400. has 4 significant
figures (Rule #5)
Calculating with Significant Figures (sig figs)
- When adding or subtracting use the least precise
place value to determine the significant
- When multiplying or dividing use the number of
significant digits in the value with the
fewest significant digits.
- Don't use counting numbers for determining
- Don't use numbers from definitions for determining
225.0 + 1.453 = 226.453 =
226.5 (Rule #1)
(1.256)(2.42) = 3.03952 =
3.94 (Rule #2)
Practice is the number one thing that you can do to master
significant figures but this is a skill well worth the effort.