1. Significant Figures There are two kinds of numbers in the world: Exact
There are exactly 12 eggs in a dozen
Most people have exactly 10 fingers and 10 toes
Inexact
Any measurement

2. If I quickly measure the width of a piece of notebook paper, I might get
220 mm 2 significant figures
If I am more precise
216 mm 3 significant figures
Even more precise
215.6 mm 4 significant figures

3. Precision vs. Accuracy Accuracy Precision
Refers to how closely a measured value agrees with the correct value
Precision
Refers to how closely individual measurements agree with each other.
Accurate and precise
Accurate but not precise
Precise not accurate

4. Significant Figures
Significant figures are critical in any measurement.
The number of sig. figs. is the number of digits believed to be correct by the person doing the measuring.
The measurement always includes one estimated digit.

5. Significant Figures 4.5 cm
When we measure something, we can (and do) always estimate between the smallest marks
4.5 cm
estimate

6. Sig Figs
The better the measuring device the better we can estimate
Remember the last number measured is an estimate
4.55 cm
estimate

7. Sig Fig Rules Needed a set of rules to decide which zeros count.
All other numbers do count as significant figs
Which zeros count:

8. Sig Figs Which zeros count Leading zeros are never significant
significant figures
Imbedded zeros are always significant
sig figs
Trailing zeros are significant only if the decimal point is specified.
sig fig 3 x 102
sig figs x 102
sig figs x 102

9. Calculating with Sig Figs
Adding and Subtracting
The last sig fig in a measurement is an estimate.
Your answer can not be better than your worst estimate.
Last digit retained is set by the first doubtful digit.

10. Rounding Rules
Look at the number to the right, or after the one you are rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make the one you are rounding one bigger
Round to four sig figs
To three sig figs
To two sig figs
To one sig fig

11. Multiplication and Division
Rule is simpler
Same number of sig figs in the answer as the least in the question
3.6 x 653
2350.8
3.6 has 2 sig figs and 653 has 3 sig figs
Answer can only have 2 sig figs
2400