Significant Figures A tutorial adapted from

What are significant figures? Significant figures are a way of expressing precision in measurement. In a measurement in lab, the digits which you can read for certain, plus one uncertain digit, are significant. Significant figures are a way of expressing precision in measurement. In a measurement in lab, the digits which you can read for certain, plus one uncertain digit, are significant.

For instance, on the graduated cylinder shown to the left, you will notice that the solution is somewhere between 25 mL and 30 mL. The first digit is certain. We know it has to be 2. When reading a measurement, always read the certain plus one uncertain. Take a good guess at the uncertain digit. Probably 8. We would report the volume of liquid in this graduated cylinder to be 28 mL. These would be the significant digits. You wouldn't want to report any more. It would be foolish to try to get any more digits in this answer. We just can't be sure! For instance, on the graduated cylinder shown to the left, you will notice that the solution is somewhere between 25 mL and 30 mL. The first digit is certain. We know it has to be 2. When reading a measurement, always read the certain plus one uncertain. Take a good guess at the uncertain digit. Probably 8. We would report the volume of liquid in this graduated cylinder to be 28 mL. These would be the significant digits. You wouldn't want to report any more. It would be foolish to try to get any more digits in this answer. We just can't be sure! If the graduated cylinder had markings every mL instead of every 5, we could get even more specific. You would certainly know the first two digits of the measurement. The uncertain digit would be whatever you "guess" to be the fraction of liquid to be between the two markings. If the graduated cylinder had markings every mL instead of every 5, we could get even more specific. You would certainly know the first two digits of the measurement. The uncertain digit would be whatever you "guess" to be the fraction of liquid to be between the two markings.

Determining Significant Figures in a Measurement There are a few basic rules to remember when counting the number of significant figures in a measurement.  All non-zero numbers ARE significant.  All non-zero numbers ARE significant.  The number 33.2 contains THREE significant figures because all of the digits present are non-zero.  Zeros between two significant digits ARE significant.  Zeros between two significant digits ARE significant.  2051 has FOUR significant figures. Since the zero is between a 2 and a 5, it's significant.  Leading zeros are NEVER significant.  Leading zeros are NEVER significant.  They're nothing more than "place holders". For instance, 0.54 has only TWO significant figures because the zero is leading and a place holder also has TWO significant figures.  They're nothing more than "place holders". For instance, 0.54 has only TWO significant figures because the zero is leading and a place holder also has TWO significant figures.  Trailing zeros to the right of a decimal ARE significant.  Trailing zeros to the right of a decimal ARE significant.  There are FOUR significant digits in because the zeros are trailing to the right of the decimal. Remember, they must be there because the person measuring this value must have been able to read these numbers from the apparatus.

Trailing zeros in a whole number with the decimal shown ARE significant. Trailing zeros in a whole number with the decimal shown ARE significant.  Placing a decimal at the end of a number is usually not done. By convention, however, this decimal will indicate a significant zero. For instance, 540. indicates that the (trailing) zero IS significant. There are a total of THREE significant digits in this number. Trailing zeros in a whole number with no decimal shown are NOT significant. Trailing zeros in a whole number with no decimal shown are NOT significant.  Writing just 540 indicates that the zero is NOT significant and there are only TWO significant figures in this value. Exact numbers have an INFINITE number of significant figures. Exact numbers have an INFINITE number of significant figures.  Numbers that are definitions or exact have an infinite number of significant figures. For example1 meter = 1000 millimeters. 1 meter equals millimeters as meters equals 1000 millimeters. Both are definitions and therefore have infinite significant figures.

Practice mL mL g g 1.20 kg 1.20 kg 10 lbs 10 lbs 10.0 seconds 10.0 seconds L L mg mg g g

Using significant figures in mathematical calculations The expression "a chain is only as strong as its weakest link" explains why significant figures need to be considered when calculating. Remember, significant figures represent the accuracy of a measurement. When manipulating these measurements by adding, subtracting, multiplying, or dividing, your final answer cannot be more accurate than the numbers you started with. Your answer can only be as accurate as the measurements you start with. The expression "a chain is only as strong as its weakest link" explains why significant figures need to be considered when calculating. Remember, significant figures represent the accuracy of a measurement. When manipulating these measurements by adding, subtracting, multiplying, or dividing, your final answer cannot be more accurate than the numbers you started with. Your answer can only be as accurate as the measurements you start with.

Multiplication and Division When multiplying or dividing, count how many significant figures are in each measurement. Your final answer should contain the same number of significant figures as which ever starting value has the least. When multiplying or dividing, count how many significant figures are in each measurement. Your final answer should contain the same number of significant figures as which ever starting value has the least. For example, when you take cm X 1.3 cm, your two measurements have 4 significant figures and 2 significant figures. Since the LEAST number of significant figures is 2, your final answer can only have 2 significant figures. For example, when you take cm X 1.3 cm, your two measurements have 4 significant figures and 2 significant figures. Since the LEAST number of significant figures is 2, your final answer can only have 2 significant figures.

Addition and Subtraction When adding or subtracting, you must count decimal places instead of significant figures. Your final answer should contain the same number of decimal places as which ever starting value has the least. When adding or subtracting, you must count decimal places instead of significant figures. Your final answer should contain the same number of decimal places as which ever starting value has the least. For example, = which rounds to 18.3 using 1 decimal place For example, = which rounds to 18.3 using 1 decimal place

Practice / / g g g g 2.11 X X X 200. X X 200. X 13.8