1. Chapter 2
Section 3

2. Measuring & Calculating
No experimentally obtained value is exact
Human errors
Method errors
Instrument errors

3. Measurements
Errors can arise depending on the instrument that is used.
It is important to use the right instrument
Would you use a balance that is calibrated to 1 g to weigh g of a substance?
Which graduated cylinder would you use from Figure 2-7 to measure 8.6 mL

4. Accuracy vs. Precision 2 things to consider when making a measurement
What is the difference between accuracy and precision?

5. Accuracy vs. Precision Accuracy: How exact it is
The extent to which a measurement approaches the true value of a quantity
Example:
You measure 35.8 ML
Lab partner measures 37.2 mL
True volume = 36.0 mL
Your measurement is more accurate than your lab partner’s

6. Accuracy vs. Precision Precision:
How closely several measurements of the same quantity made in the same way agree with each other
Measure the mass of a substance four times using the same balance
110 g, 109 g, 111 g, and 110 g.

7. Accuracy vs. Precision
The measurements were close to each other so they are precise
Remember that precise measurements are not always accurate measurements
Ex:
If the balance was not reset to zero the measurements are close to each other (precise) but not but not accurate

8. Significant Figures Significant Figures:
Measurement or calculation that consists of all the digits known with certainty plus one estimated or uncertain digit
Ex:
g is accurate to 5 places
The 6th place is the estimated digit

9. Significant Figures
Using the markings on the thermometer we can estimate the temperature to be 28.4 degree C
28.4 is 3 significant figures
The first two digits we know for certain
The third digit is an estimate
The actual temperature is between 28.2 and 28.6
Report the measurements with the correct number of significant figures
Example:
Measuring temperature with a thermometer marked in intervals of 1 degree C

10. Significant Figures
Burets vs. Graduated Cylinders

11. Significant Figures Buret vs. Graduated Cylinder
100 mL graduated cylinders are calibrated to the nearest 1 mL
Burets are calibrated to the nearest 0.1 mL
Best measurement with a graduated cylinder is 25.0 mL – uncertainty is in the tenths place
Best measurement with a buret is mL – uncertainty is in the hundredths place

12. Rule
Example
Zeroes appearing between nonzero digits are significant
40.7 has 3 significant figures
87009 has 5 significant figures
Zeroes appearing in front of nonzero digits are not significant
has 4 significant figures
has 1 significant figure
Zeroes at the end of a number and to the right of a decimal point are significant
85.00 g has 4 significant figures
has 10 significant figures
Zeros at the end of a number with no decimal point may or may not be significant. Read the rest of 4 in the book
2000 may contain 1-4 significant figures
2000. Has 4 significant figures

13. Significant Figures
Be careful when calculating with significant figures
Ex: Mass of a 32.4 mL sample = g
If we used this information to determine density D = m/v we would get g/mL
The volume has 4 significant figures while the mass has 3 and the density has 10
So what do we do?

14. Operation Rule Example
Multiplication and Division
The answer can have no more significant figures than there are in the measurement with the smallest amount of significant figures
12.257 X
________
Answer = 14.24
Addition and Subtraction
The 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
3.95
2.879
Answer = 220.4

15. Significant Figures Multiplication and Division
The answer should have the same number of significant figures as the measurement with the least amount of significant figures
Do NOT round until the end when doing calculations

16. Significant Figures Addition and Subtraction
The answer can have no more digits to the right of the decimal than there are in the measurement with the smallest number of digits to the right of the decimal
Remember it is only significant figures to the right of the decimal not total significant figures

17. Significant Figures Exact value: Value that has no uncertainty
Has an unlimited number of significant figures
2 categories of exact values
Count Values
Conversion Factors

18. Significant Figures Count Values
Value that is determined by counting and not by measuring
Example a water molecule has 2 hydrogen atoms and 1 oxygen atom
No uncertainty in this value because we count the number of atoms NOT measure them

19. Significant Figures 2. Conversion Factors 1 m = 1000 mm
No uncertainty because a millimeter is determined as exactly one-thousandth of a meter
1 mm = m
Exact values ALWAYS have more significant figures than any other value in the calculation
Never use counted or conversion factors to determine the number of significant figures in your calculated results

20. Scientific Notation
Very large and very small numbers are written in scientific notation
2 parts to each value written in scientific notation
1. Number between 1 and 10
2. A power of 10

21. Scientific Notation 1st part: 2nd part:
Move the decimal to the right or left so only 1 nonzero digit is to the left of it
2nd part:
Exponent
Determined by counting the number of decimal places the decimal point must be moved.

22. Scientific Notation
If the decimal point is moved to the left the exponent is positive
If the decimal point is moved to the right the exponent is negative
Eliminates the need to count zeroes

23. Examples are in the Book page 63
Table 2-6
Examples are in the Book page 63
Rule
Addition & Subtraction: All values must have the same exponent before they can be added or subtracted. The result is the sum or difference of the first factors all multiplied by the same exponent of 10.
Multiplication: The first factors of the numbers are multiplied and the exponents of 10 are added
Division: The first factors of the number are divided, and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator

24. Scientific Notation Table 2-7 on page 64
Questions to Check for Learning
Page 64 Problems 5-10 and 12

25. Additional Problems
1. Determine the # of significant figures in each of the following quantities
218 kPa
0.025 L
200. m2
1.05 g

26. Additional Problems
2. Round the following quantities to the # of significant figures indicated in parentheses
km (3)
155.8 g (3)
cm (2)
12000 kPa (3)