Significant Figures There are two kinds of numbers: Exact Inexact Example: There Example: Any are twelve eggs measurment in a dozen
If I were to measure a piece of paper, I might get 20.15 mm You might get 20.14 mm. Somebody else may get 20.16 Who is right ????? Precision vs. Accuracy Accuracy Precision
- Refers to how - Refers to how closely individual measurements agree with each other closely a measured value agrees
with the correct value Remember..there is uncertainty in all measurement but the precision is determined by the measuring device. In any measurement, the number of significant figures is the number of digits believed to be correct by the person doing the measuring It also includes one estimated digit.
Here are 3 examples of when sig. figs. are important when measuring volumes in the lab. A beaker A graduated cylinder
A buret A rule of thumb: Volumes should be read to 1/10 of the smallest division. Example: If the smallest division is 10 mL, the volume would be read as having an error of 1 mL. A Beaker
The smallest division is 10 mL-so we can read the volume to 1 mL. The volume in the beaker is 47(+ or ) 1mL. It might be 46it might be 48. So, how many sig. figs.???? (2) - The 4 we know for sure, plus the 7 that we had to
estimate. A Graduated Cylinder
The smallest division is 1 mL so we can read the volume to 0.1 mL. The volume could be read as 36.5 (+ or -) 0.1 mL. The true volume could be 36.4 or 36.6. How many sig. figs??? (3)- The 3 and 6 we know for sure- the 5 had to be estimate. A Buret
The smallest division is 0.1 mL so we can read the volume to 0.01 mL. A good volume reading would
be 20.38 (+ or -) 0.01 mL. An equally precise answer would be 20.39 or 20.37. How many sig. figs.???? (4)- The 2, 0, and 3 we know for sure, the 8 we had to estimate. Conclusion: Significant figures are directly linked with measurement. Now, how do we determine significant figures?
Determining the number of sig. figs. in a number. Picture a map of the U.S. If a decimal point is present, count from the Pacific side. Start counting with the first nonzero digit. All digits from here to the end, including zeros, are significant. Examples:
Significant Figures in Calculations: Rules for Multiplication and Division The answer contains no more significant figures than the lease accurately known number. Examples: The number with the
least # of sig. figs. has 2 sig. figs. Therefore, the answer must have 2. The number with the least # of sig. figs. has 3 sig. figs. Therefore, the answer must have 3. Rules for Addition and Subtraction The number of sig. figs. is determined by the location of
digits in the number with the largest uncertainty, not the number of significant figures in the number. Examples: The least precise number is 2.02. It has sig. figs. out to the hundredths place. Therefore the answer will have sig. figs. out to the hundredths
place. The least precise # (1.0236) has decimals carried out 4 places. Therefore the answer will have sig. figs. carried out 4 decimal places.
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