CHM102 Lecture Notes - Lecture 2: Carbon-12, Significant Figures
Significant Figures
- Measured quantities are generally reported in such a way that only the last digit
is uncertain.
- E.g. 4.0 g and 4.00 g imply different levels of uncertainty in the measurement. i.e.
4.0 ± 0.1 g and 4.00 ± 0.01 g
- To work out how many significant figures, count from left to right, starting with the
first number that is not zero.
- Zeros may or may not be significant, depending on how they appear in the
number.
Rules for Significant Figures in Answers
1. For addition and subtraction.
- Answer has the same number of decimal places as there are in the
measurement with the fewest decimal places.
- For addition and subtraction the NUMBER of SIGNIFICANT FIGURES CAN
CHANGE!
2. For multiplication and division.
- Number with least certainty limits the certainty of result.
- So, answer contains the same number of sig figs as are in the measurement with
the fewest significant figures.
3. Combined addition/subtraction and multiplication/division
- You will usually need to do the addition/subtraction first, round to the appropriate
number of decimal places, and then the multiplication/division, and round to the
appropriate number of sig figs.
- Note this is the opposite of the mathematical order of operations!
3. Combined addition/subtraction and multiplication/division
Example: Calculate the density for the following solution:
Final volume. 12.72 mL
Initial volume: 10.01 mL
Mass of sample: 3.546g
Density = 1.31 g/mL
Document Summary
Measured quantities are generally reported in such a way that only the last digit is uncertain. 4. 0 g and 4. 00 g imply different levels of uncertainty in the measurement. i. e. 4. 0 0. 1 g and 4. 00 0. 01 g. To work out how many significant figures, count from left to right, starting with the first number that is not zero. Zeros may or may not be significant, depending on how they appear in the number. Rules for significant figures in answers: for addition and subtraction. Answer has the same number of decimal places as there are in the measurement with the fewest decimal places. For addition and subtraction the number of significant figures can. Number with least certainty limits the certainty of result. So, answer contains the same number of sig figs as are in the measurement with the fewest significant figures: combined addition/subtraction and multiplication/division.
