1. Measurement: Significant Figures

2. Precision and Accuracy
Low Accuracy High Precision
High Accuracy High Precision
High Accuracy Low Precision

3. Significant Figures
Significant Figures (sig. figs.): the number of digits that carry meaning contributing to the precision of a measurement or calculated data.

4. Significant Figures
The significance of a digit has to do with whether it represents a true measurement or not.
Any digit that is actually measured or estimated will be considered significant.
Placeholders, or digits that have not been measured or estimated, are not considered significant.

5. Significant Figures
There are 5 rules to determine which digits in a measurement or number are significant or not.

6. Rules for Significant Figures
Rule #1: All non-zero digits (1-9) are significant. For example: 453 number of sig figs______ number of sig figs______

7. Rules for Significant Figures
Rule #2: Zeros between non-zero digits are significant. For example: number of sig figs______ number of sig figs______

8. Rules for Significant Figures
Rule #3: Zeros to the left (“leading” zeros) of the first non-zero digit are NOT significant. For example: number of sig figs______ number of sig figs______ number of sig figs______ number of sig figs______

9. Rules for Significant Figures
Rule #4: If a number ends in zeros (“lagging” zeros) to the right of the decimal point, those zeros are significant. For example:
2 number of sig figs______ number of sig figs______ number of sig figs______ number of sig figs______
{This signifies greater precision.}

10. Rules for Significant Figures
Rule #5: If a number ends in zeros (“lagging” zeros), the zeros to the right are NOT significant IF there is NO decimal point present. For example: number of sig figs______
number of sig figs______ number of sig figs______

11. Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 98070001) 2) 3) 4) 5) 6) 7) 8)
Ex 1) (5 sig. figs.)
Ex 2) (4 sig. figs)
1) (5 sig. figs.)
2) (4 sig. figs.)
3) (4 sig. figs.)
4) (5 sig. figs.)
5) (2 sig. figs.)
6) (5 sig. figs.)
7) (7 sig. figs.)
8) (6 sig. figs.)

12. Calculations with Sig Figs
Add and subtract:
Answer gets rounded based on the fewest decimal places from question
Example:
The last 6 isn’t significant because the fewest decimal places in the Q is the third

13. Calculations with Sig Figs
Multiply and Divide:
Answer gets rounded to fewest significant figures from the question
44 x 20 = 880
Round to 900 because one of the values in the question only has one sig fig

14. Answers to Significant Figure Calculation Practice
2) 3.4 g/ml 3)
4) m
5) 450. cm
6) 0.28 m/s
7) kg
8) 900 m