1. “Uncertainty in Measurement”
A measurement always
involves a comparison of
known vs. unknown
Exact numbers have values that are known exactly (given from a textbook)
Inexact numbers have values that include some level of uncertainty (measurements)
Linked

2. “Precision & Accuracy”
Linked

3. Different measuring tools may have differing levels of certainty

6. Significant Figures
All digits of a measured quantity, including the uncertain one, are called significant
“If you measured it (even though you may be uncertain) it is significant or meaningful to you!”

7. Counting Significant Figs
1) All nonzero digits are significant.
Zeros in-between significant figures are significant.
Zeros beyond the decimal point at the end of a number are significant.
4) Zeros preceding the first significant figures in a number are NOT significant.

8. Counting Significant Figures
How many sig figures do the following #s have?
23.2 cm g
50.00 mL s
g g

9. Rounding Off Nonsignificant Figs
If a calculator displays and only 3 significant figures are justified, what would you round to?
Beware of “Place-Holder Zeros” !!!
Round off to 2 sig figs?
Round off to 3 sig figs?

10. Rounding Off Nonsignificant Figures
If the first nonsignificant figure is less that 5, drop all nonsignificant figure
If the first nonsignificant figure is ≥5, increase the last significant figure by 1 and drop all nonsignificant figures.
If a calculation has 2 or more operations, retain the nonsignificant figures until the final operation.

11. Calculations using Sig Figs
Addition/Subtraction
The result must have the same number of decimal places as there are in the measured quantity with the smallest number of decimal places
(the answer is limited by the measured value with the most uncertainty)
12 g g g = 36.11g
apply the rule and round and the answer is 36 g

12. Adding/Subtracting Sig Figs
8.6 cm cm =
– = =
– 21.1 =

13. Calculations of Measurements
Multiplication/Division
The result must have the same number of significant figures as there are in the measured quantity with the smallest number of significant figures
( mg) / (9.0210mL)= mg/mL
apply the rule and round and the answer is mg/mL

14. Multiplying and Dividing Sig Figs
(134.75)(25.83)(3.23) =
( ) ÷ ) =
(95.86)(2.117)(15.3)
(874.11)(11.312)(77.22) =