1. Measurements and their Uncertainty
Chapter 3.1
Measurements
and their Uncertainty

2. Using and expressing measurements
Measurement = a quantity that has both a number and a unity
**Measurements are fundamental to the experimental science! Therefore, it is important to be able to make measurements and to decide whether a measurement is correct.**

3. Using and expressing measurements
International System of Measurement = SI
These are the units typically used in Science
Meter, kilogram, second, Kelvin, etc.

4. Scientific Notation
Where a given number is written as the product of 2 #’s: a coefficient and 10 raised to a power
Why??
Writing large numbers is prevalent in Science and very cumbersome.
Ex) 1 g Hydrogen = 602,000,000,000,000,000,000,000 H atoms
-or-
6.02 x 10 23
Coefficient = 6.02
Exponent = 23

5. Scientific Notation
Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction.

6. Scientific Notation

7. Accuracy & Precision
Accuracy = a measure of how close a measurement comes to the actual or true value.
Precision = a measure of how close a series of measurements are to one another.

8. Accuracy & Precision
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.
To evaluate the precision of a measurement, you must compare the values of 2 or more repeated measurements.

9. Accuracy & Precision

10. Accuracy & Precision

11. Error
Accepted (true) Value = the correct value based on reliable references
Experimental value = the value measured in the individual situation
Error = the distance between the accepted value and the experimental value.

12. Error
Percent error = the ratio of an error to an accepted value.

13. Significant figures
A number that includes all of the known digits plus one estimated digit.
Measurements must always be reported to the correct # of significant figures because calculated answers often depend on the # of significant figures in the value used in calculation.
See page 67 in text for meter sticks with different callibrations!!

14. Significant Figures Rules for recognizing significant figures
Non-zero numbers are always significant.
72.3 g has three
Zeros between non-zero numbers are always significant.
60.5 g has three
All final zeros to the right of the decimal place are significant.
6.20 g has three

15. Significant Figures Rules for recognizing significant figures
Zeros that act as placeholders are not significant. Convert quantities to scientific notation to remove the placeholder zeros.
g and 4320 g each have three
Counting numbers and defined constants have an infinite number of significant figures.
6 molecules 60 s = 1 min

16. Significant Figures in Calculations
A calculated answer cannot be more precise than the least precise measurement from which it was calculated!

17. Significant Figures in Calculations
Addition & Subtraction
Round the answer to the same # of decimal places as the measurement with the least # of decimal places.
The answer is 77.2

18. Significant Figures in Calculations
Multiplication & Division
Round the answers to the same # of sig. figs as the measurement with the least # of sig figs.

19. Multiplication & Division With Sig. figs
Calculate the volume of a rectangular object with the following dimensions:
length = 3.65 cm width = 3.20 cm height = 2.05 cm
The answer is 23.9 cm3.