1. Accuracy vs. Precision & Significant Figures

2. Why Accuracy and Precision is Important
Measurements must be made with standard instruments using standard procedures!
If not we may get errors, limitations, and inaccuracies

3. Accuracy
Accuracy is the extent to which a measurement approaches the true value of a quantity
Deals with how exact the measurement is to the true value
Ex: 35.8 mL 37.2 mL actual=36.0 mL
(35.8mL is more accurate)

4. Precision
Extent to which a series of measurements of the same quantity made in the same way agree with one another
Deals with how close the numbers agree
Ex: 110 g, 109 g, 111 g, 110 g

5. 1. 2. 3. 4.

6. Significant Figures
Any digit in a measurement that is known with certainty plus one final digit, which is somewhat uncertain or estimated
AKA “Sig Figs”
EX: g (11.68 is known)
(0.007 is the estimated digit)

7. Rules of Determining Sig Figs
Nonzero digits are always significant
Ex: Sig Figs
Zeros Between nonzero digits are significant
Ex: Sig Figs
Zeros in front of nonzero digits are not significant
Ex: Sig Fig
Zeros at the end of a number and to the right of a decimal point are significant
Ex: Sig Figs
Zeros at the end of a number with no decimal point are not significant
Ex: Sig Fig
A decimal place after zeros means all numbers are significant
Ex: Sig Figs

8. How Many Sig Figs?
31.9
859.00
20.5
4000
3000
300.
2013 18
6000. 10
13.175
10.00
50,000,000 3

9. Calculations Involving Significant Figures
Do not round until after you have the end number
Multiplication & Division
Round the calculated result to the same number of sig figs as the measurement having the least number of sig figs
Ex: x =
(3 sf’s) (2 sf”s) must be rounded to 2 sf’s
rounded answer =13

10. Calculations Involving Significant Figures
Addition and Subtraction
Answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point
Ex: 3.95
2.879
213.6
round to 220.4

11. Solve With the Correct Amount of Sig Figs?
a) / 5.12 =
193
5 sf’s
3 sf’s
3 sf’s
8 sf’s

12. Solve With the Correct Amount of Sig Figs
3 #’s after decimal
2 #’s after decimal
4 #’s after decimal
27.343
6.09
2 #’s after decimal
4 #’s after decimal
46.56 ?

13. Scientific Notation
A way of writing very large or very small numbers in a way that is easier to calculate and takes up less space
Contains a number between 1-10 and a power of 10
Move decimal left = positive exponent
Move decimal right = negative exponent
EX:
= 6.02 x 1023
= 7.85 x 10-17

14. Calculations with Scientific Notation
If numbers in scientific notation are multiplied exponents are added
Ex: (4.2 x 102) (3.9 x 105) = 16 x 107
If numbers in scientific notation are subtracted exponents are subtracted
Ex (8.2 x 107) / (4.1 x 104) = 2.0 x 103