1. Measurement Unit Unit Description:
In this unit we will focus on the mathematical tools we use in science, especially chemistry – the metric system and moles.
We will also talk about how to gauge the accuracy and precision of our measurements.

2. Measurement Unit The Big Questions
How do we measure things in chemistry?
Why are units so important?
How accurate and precise are my measurements and how can I show this in my calculations?
How can I move between different measurement units?
What the heck are moles and why are they important?

3. Measurement Unit Review Topics: scientific notation and exponents
metric system
algebra
density calculations
dimensional analysis – conversions
temperature conversions

4. Measurement Unit New Topics:
rounding in chemistry – significant figures
determining uncertainty of a measurement
% error
accuracy vs. precision

5. Measurement Unit
New Topics:
Moles!
and related topics…

6. Accuracy and Precision
Accuracy = how close one comes to the actual value (absolute error)
Precision = the agreement of two or more measurements that have been made in the same way (reproducibility)

7. Accuracy and Precision
Can you have accuracy without precision? Or precision without accuracy? Why or why not?

8. Neither accurate nor precise  

9. Precise but not accurate 

10. More accurate but not precise 

11. Both precise and accurate, the sweet spot 

12. What are significant figures and why do we use them?
Measurements are dependent on the instruments we use.
We round our measurements to reflect the level of precision of these instruments.
These are significant figures.

13. Significant Figures in Measurement
consist of all parts of the measurement that you know for sure + one estimated digit e.g. metric ruler, thermometer

14. Pacific/Atlantic Rule
If decimal is Present, start counting at the first non zero digit on the left, go all the way to the end
If decimal is Absent, start counting at the first non zero digit on the right, go all the way to the end
Pacific Ocean
Atlantic Ocean

15. Rules for Recognizing Significant Figures
Non-zero numbers are always significant.
Zeros between non-zero numbers are always significant. i.e. 101, .101
All final zeros to the right and left of the decimal place (i.e. after digits) are significant.
i.e. .30 and 30.

16. Rules for Recognizing Significant Figures
4. Zeros that act as placeholders are not significant. i.e. 3000, .003 Convert quantities to scientific notation to remove the placeholder zeros. 3x104, 3x Counting numbers and defined constants have an infinite/unlimited number of significant figures. i.e. gas constant, avogadro’s number

17. How many sig figs are in the following measurements?

18. How many sig figs are in the following measurements?

19. Rules for Rounding Numbers
If the digit to the immediate right of the last significant figure is
< 5, do not change the last significant figure.
2. > 5, round up the last significant figure.

20. Rounding Practice:
Round the following measurements to two sig figs: 13.4 g 13.5 g g 14.5 g g g g 10.5 g

21. Rounding Practice:
Round the following measurements to two sig figs: 13.4 g 13 g 13.5 g 14 g g 14 g 14.5 g 15 g g 15 g g 15 g g 15 g 10.5 g 11. g

22. Significant Figures What about electronic instruments?
e.g. electronic balances, digital thermometers
The electronics within the instrument estimate the last digit.

23. Addition and Subtraction
You cannot be more precise than your last uncertain number. If the mass of something weighed on a truck scale was added to the mass of an object weighed on one of our centigram balances, the sum would NOT be precise to 0.01 g.

24. Addition and Subtraction
If you circle the uncertain number (which is significant), it can be seen that in additions and subtractions, you round off to the left-most uncertain number.

25. Addition and Subtraction
e.g   31.1 Align the decimal places, perform the calculation, then round off to the least significant decimal place.

26. Multiplication and Division
The product or quotient is precise to the number of significant figures contained in the least precise factor.
e.g. 1:
63.2 cm x 5.1 cm = cm2  cm2 (2 sfs)
e.g. 2:
5.30 m x m = m2  0.03 m2 (1 sf)

27. Sig Fig Practice Addition/Subtraction and Multiplication/Division
1. Calculate and round to the correct number of sig figs.
a) 4.53 x 0.01 x 700 =
b) 2 x 4 x =
c) _0.01_ =
0.0001
d) =
e) – =
( ) =
(4.32 x 1.7)

28. More Sig Fig Practice Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and express each result to the correct number of significant figures mL mL mL mL = 4 (this is an averaging calculation) 2. (8.925 g – g) x 100% = g 3. (9.025 g/mL – g/mL) x 100% = g/mL

29. More Sig Fig Practice (Honors) Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and express each result to the correct number of significant figures.
x x ( ) =
5. (9.04 – ) ¸ =
(4.987 – 4.962) =
1.285 x x x =
( – ) =
x 1023

30. Scientific Notation
Scientific Notation is way of dealing with very large or very small numbers
Written in two parts:
Just the significant digits (always with only one digit to the left of the decimal place)
Multiplied by a power of 10

31. Rules for Scientific Notation
The base is always 10!
The exponent is always a +(for big numbers) or –(for small numbers) integer
The coefficient is always >1 and <10
The coefficient carries the sig figs

32. To “un do” scientific notation
If the exponent is +, move decimal place to the right
If the exponent is -, move decimal place to the left

33. Examples of Scientific Notation
185,000 = 1.85 × 105
= 2.3 × 10-3
To figure out the power of ten, think about whether the decimal needs to move to the left or right, and how many places it needs to move
When the number is 10 or greater, the decimal point has to move to the left, and the power of 10 is positive.
When the number is smaller than 1, the decimal point has to move to the right, so the power of 10 is negative.

34. Uncertainty in Measurement
The last place of a measurement is always an estimate.
The size of the estimate is based on the reliability of the instrument
 range within which the measured value probably lies

35. Uncertainty in Measurement
Report to only one sig fig.
That digit should be in the same decimal place as the last sig fig of the measurement.
Correct
Incorrect
36.5 ± 0.5 m
36.5 ± m
300.4 ± 0.2 g
300.4 ± 0.05 g
230 ± 10 s
232.4 ± 5 s

36. Uncertainty in Measurement
Report to only one sig fig.
That digit should be in the same decimal place as the last sig fig of the measurement.
Correct
Incorrect
36.5 ± 0.5 m
36.5 ± m
 36.5 ± 0.2 m
300.4 ± 0.2 g
300.4 ± 0.05 g
 ± 0.1 g
230 ± 10 s
232.4 ± 5 s
 230 ± 5 s

37. Percent Error “what you should have got”
|theoretical – actual| x 100% = ___ %
theoretical
“what you should have got” – “what you got” x 100
“what you should have got”