1. Today is Wednesday, September 13th, 2017
In This Lesson:
Measurement and Significant Figures
(Lesson 3 of 6)
Stuff You Need:
Calculator
Today is Wednesday, September 13th, 2017
Pre-Class:
Get your calculators and get ready.
Something else to do:
What would it mean if I told you that when it comes to basketball, I’m not very accurate but I am very precise?
Last thing:
Today (or maybe next class) I will teach you how 5 x 5 = 30.

2. Today’s Agenda Measurement Significant Figures
Where is this in my book?
P. 62 and going for quite a few pages…

3. By the end of this lesson…
You should be able to differentiate between accuracy and precision.
You should be able to determine which digits of a number are significant.

4. Measurement
Yes, in the world of chemistry, even a term such a measurement has a distinct definition.
A measurement is a quantitative observation that consists of two parts:
Number
Scale (unit)
If you leave out either one, I must deduct points.
For example:
21 grams
6.63 x Joule seconds

5. Uncertainty
As it turns out, not every measurement is perfectly accurate.
In any measurement there’s a degree of uncertainty.
For example, how many mL do you see here?
53 mL sounds good, but you can estimate one more digit mL?
(In this class, you should estimate that extra digit)

6. Accuracy versus Precision
In addition to uncertainty, measurements also can be judged according to their accuracy or their precision.
What’s the difference?
Accuracy is how close a measurement comes to reality.
Precision is how “repeatable” a measurement is or the number of decimal places an instrument measures.
“60% of the time, it works every time.”

7. Accuracy versus Precision1. 2.
High Accuracy,
High Precision
High Accuracy, Low Precision
Low Accuracy,
High Precision
Low Accuracy, Low Precision 3. 4.

8. Accuracy and Precision
Suppose you have an electronic balance that provides measurements to two decimal places.
It’s certain to two. Other digits are uncertain.
If the balance always gives you the same mass for the same object, it’s precise.
If it gives you the right mass, it’s accurate.
Are there ways in which it could be accurate but not precise?
How about precise but not accurate?

9. Pre-Class Part Deux
Facebook was recently reported to have 1.6 billion users1.
Is it exactly 1,600,000,000?
Could it possibly be 1,600,000,001?
Why is it okay to just say 1.6 instead of all the zeroes?
If you needed to calculate the circumference of a circle but you only knew the diameter was 8, what would you do?
Most of us would multiply by pi (π).
How much is pi, again?
1Bloomberg Business Week – March 24, 2016

10. Significant Figures
Scientists need to be clear with one another about how many digits to which they are rounding.
In other words, they need to be clear about the level of uncertainty they’re willing to accept.
One scientist may say pi is 3.141, another may say
To determine how many digits your answer should be, we use significant figures.
Significant figures are the “digits that count” – overall, they’re used as a special form of rounding.
Also known as Significant Digits, or Sig Figs, or Sig Digs.

11. 4 Rules for Counting Sig Figs
If the number contains a decimal point, count from right to left until only zeros or no digits remain.
Examples: grams
4 sig figs
meters
5 sig figs
grams
2 sig figs

12. 4 Rules for Counting Sig Figs
If the number does not contain a decimal point, count from left to right until only zeros or no digits remain.
Examples: 255 meters
3 sig figs
1,000 kilograms
1 sig fig

13. Quick Interlude: Oceanic Sig Figs
Here’s a way to remember Rules 1 and 2, although it doesn’t work in Hawaii:
If there is a decimal point present, count in the direction of the Pacific (to the left).
If the decimal point is absent, count in the direction of the Atlantic.

14. 4 Rules for Counting Sig Figs
For numbers in scientific notation (M x 10n), count only the sig figs in the M number – use rules 1 and 2 normally.
Examples: x cm
3 sig figs
2 x 105 g
1 sig fig

15. 4 Rules for Counting Sig Figs
Exact numbers and percentages have an infinite number of significant figures.
Rare in this class (usually for unit conversions).
1 inch = 2.54 cm exactly
1 dozen = 12 eggs-actly

16. Counting Sig Figs 1.0070 m = 5 sig figs 17.10 kg = 4 sig figs
How many significant figures in each of the following?
m =
5 sig figs
17.10 kg =
4 sig figs
100,890 L =
5 sig figs
3.29 x 103 s =
3 sig figs
cm =
2 sig figs
3,200,000. =
2 sig figs (the decimal point needs digits after it to count)

17. Now for some practice…
Significant Figures in Measurements and Calculations
Part I – choose 15.
Difficult and/or Scientific Notation:
13, 14, 18-20
The competition will be afterward!

18. Now for a break…
Let’s take a look at some pretty interesting uses of measurements (particularly in terms of accuracy).
Parallel Parking video.

19. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction:
The number of digits after the decimal point in the result equals the number of digits after the decimal point in the least precise measurement.
Round the “end” normally. =
=  18.8

20. Adding and Subtracting
Calculation
Calculator says:
Answer
3.24 m m
10.24 m
10.2 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL

21. Now for some practice…
Significant Figures in Measurements and Calculations
Part II – choose 5.
Part III – choose 3.
Difficult and/or Scientific Notation:
28, 30
The competition will be afterward!

22. Rules for Significant Figures in Mathematical Operations
Multiplication and Division:
The number of significant figures in the result equals the number of significant figures in the least precise measurement used in the calculation.
Round the “end” normally.
6.38 x 2.0 =
6.38 x 2.0 =  13 (2 sig figs)

23. Multiplying and Dividing
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
23 m2
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
240 m/s
lb x 3.23 ft
lb·ft
5870 lb·ft
1.030 g x 2.87 mL
g·mL
2.96 g·mL

24. Now for some practice…
Significant Figures in Measurements and Calculations
Part IV – choose 5.
Part V – choose 3.
Difficult and/or Scientific Notation (you must try one of these):
45, 46, 48, 50, 51, 55
The competition will be afterward!

25. Closure So, using sig fig rules, solve this problem:
5 x 5 = ?
5 x 5 = 30
Now solve this one:
5.0 x 5.0 = ?
5.0 x 5.0 = 25

26. Closure Part Deux Try this one: 15 g x 4.0 g = ?
15 g x 4.0 g = 60 g…but it needs to be 2 sig figs!
15 g x 4.0 g = 60.0 g…is 3 sig figs!
Write this down: When in doubt, make it scientific notation (we’ll do this later).
6.0 x 101 g2

27. Final FYI What about something like percent error?
You’re doing both subtraction and division, so which rule(s) apply?
The answer is that multiplication/division trump addition subtraction.
So use the “least number of sig figs” rule.

28. More sig fig practice: Do this: Then try 10:
Then try 10:

29. Transition
CrashCourse – Unit Conversion and Significant Figures