1. Bellwork 9/8: Mind your SF
Find the volume of a cube that is 3.23 cm on each edge.
Calculate the density of a g object that occupies 4.13 cm3.
Calculate the volume of that same object but with a mass of 10.4 g.
Calculate the density of a sample with a mass of g and a volume of 2.3 mL.
What is the volume of that same sample but with a mass of g?
33.7 cm3
4.35 g/cm3
If a liquid has a density of 1.17 g/cm3, how many liters of the liquid have a mass of 3.75 kg? A: 3.21 L

2. Bellwork
A plastic ball with a volume of 19.7 cm3 has a mass of 15.8 g. What is its density? Would this ball sink or float in a container of gasoline? (Gasoline’s density is g/cm3.)
A shiny, gold-colored bar of metal weighing 57.3 g has a volume of 4.7 cm3. Is the metal bar pure gold? (The density of gold is 19 g/cm3.)
How many SF are in the following:
3000 ____ ___ ____
3000. ____ ___ m ___
Solid paraffin sinks in melted paraffin, but ice floats in water. What does this tell you about the densities of each of these substances in the solid & liquid states?
Solid paraffin is denser than its liquid but ice is less dense than liquid water.
g.cm3; it would sink

3. Activity time! Find the thickness of a square piece of aluminum foil.
Think about how you could do this – with what we have…
When you’re ready, write your procedure and let me check it… Then you can proceed with the calculation.

4. Measure the area and mass of your foil.
Use the density of aluminum estimated 2.70 g/cm3.

5. Using scientific measurements
Chapter 2 Section 3
Scientific notation starts at #54
Using scientific measurements

6. Let’s try this out…
Use your calculator to find the volume of one gram of aluminum if 15 grams have a volume of 41 cm3.
cm3 write on the board

7. But do we really know this measurement to the nearest ten-millionth of a gram?! It’s really important to have rules that specify which digits should be kept in an answer. Calculators aren’t programmed to display the correct number of “meaningful” digits.

8. Objectives Distinguish between accuracy and precision.
Determine the number of significant figures in measurements.
Perform calculations involving sig figs.
Convert measurements into scientific notation.

9. Accuracy and Precision
Using Scientific Measurements
Chapter 2
Accuracy and Precision
Good accuracy – good precision
Poor accuracy – good precision
Poor accuracy – poor precision

10. Accuracy refers to how close a measurement is to the correct or accepted value of the thing measured.
Precision is the closeness of the measurement to the accepted value. It is repeatable – made in the same way.
Measured values that are accurate are close to the accepted value.
Measured values that are precise are close to one another but not necessarily close to the accepted value.

11. Accuracy & Precision
When taking measurements, your data can be precise (close to the same every time), accurate (close to the accepted value) and hopefully BOTH!

12. Error in measurement
Some error or uncertainty always exists in any measurement.
Example:
Skill of the measure-taker
Conditions of measurement
Measuring instruments

14. Significant Figures
Sig figs are the digits in a measured quantity that reflect the uncertainty in the measurement.
The number of digits indicates the precision of the measurement.
Precision is the closeness of the measurement to the accepted value. It is repeatable – made in the same way close it is to correct

15. Significant Figures
Sig figs in a measurement consist of all the digits known with certainty PLUS one final digit, which is somewhat uncertain or is estimated.

17. Measuring gives significance (or meaning) to each digit in the number produced. This concept of significance, of what is and what is not significant is VERY IMPORTANT. Especially the "what is not" portion. Pay close attention to sig figs in your answers because they reflect what is and what isn’t known about your measurements.

18. The takeaway…
A calculation result cannot be more precise than the least precise value used to calculate it.

19. What value should be recorded for the length of this sword?cm

20. What about this measurement?cm

21. 1) 20 cm The greater number of divisions = more precise measurement and greater # of sig figs.

22. What is the measurement of the pencil?
The graduated cylinder?

23. Significant Figures
All non-zero digits are significant ____ sf ____ sf 7.33 ____ sf 1.25 x 10-6 ____ sf Zero in the “middle” is significant ____ sf 10.5 ____ sf ____ sf 5.04 x 103 ____ sf Zero after the decimal: After the number—significant, but before the number—insignificant 3.00 ____ sf ____ sf ____ sf ____ sf Zero with no decimal—insignificant 3000 ____ sf ____ sf Zero in front of the decimal—significant ____ sf ____ sf ____ sf 10. ____sf

24. Law of Conservation of Mass

25. With a partner, try the ones in your notes…
When you’re done we’ll try a few more in the textbook.

26. Let’s try some of these…
Sample D, pg. 45
How many sig figs are in each of the following measurements?
28.6 g
3440. cm
910 m L kg

27. Answers: 3 sig figs – no zeros so all are significant
4 sig figs – 0 is significant b/c it is followed by a decimal point.
Only 2. The 0 is not significant.
The first 2 0’s are not significant, the 3rd is. There are 4 sig figs.
The first 3 0’s are not significant. The last 3 0’s are. There are 5 sig figs.

28. Practice pg. 46: 1 - 2
Then we’ll check answers.

29. Answers Pg. 46 1.a) 5 2 a) 7000 cm b) 6 b) 7000. cm c) 4 c) 7000.00 cm
d) 1
e) 5
f) 6

30. Rounding Look at the number following the number you want to keep
Round up if followed by a 5 or up
Round down if followed by a 4 or less
Round the following to 3 significant figures
42.68 g
17.32 m cm

31. Rounded to 3 sig figs
42.68 g g
17.32 m m
cm cm

32. Addition or subtraction:
The number of decimal places in the answer is the same as the number of decimal places in the measurement with the fewest decimal places.
We’ll talk about what to do when there is no decimal… when the time comes!
If there is no decimal point, round the result back to the digit that is in the same position as the leftmost uncertain digit in the quantities being added or subtracted.

33. Rules for Calculations
“decimal places”

34. Look at the ones in your notes…=
312.5 – ** change yours to this
– 3.12 =

35. = 2.0
312.5 – = 262.4
– 3.12 = -3.04

36. Rules for Calculations
Multiplication and division:
the number of sig figs in the answer is the same as the measurement with the fewest sig figs.
1) x
2) 5.0  0.055
3) 1.2  ** Change this one too
In their notes.

37. x =
2) 5.0  = 91
3) 1.2  = 240
What happens if you add a decimal there??

38. Sample E, Pg. 48
Carry out the following calculations. Express each answer to the correct number of sig figs.
5.44 m – m
2.4 g/mL x mL

39. The answer needs 2 digits to the right of the decimal point to match 5
The answer needs 2 digits to the right of the decimal point to match 5.44 m.
2.83 m is the answer.
b. For multiplication, we need 2 sig figs to match 2.4 g/mL. The answer is 38 g.

40. Try the Practice Qs
Pg. 48: 1 - 3

41. Don’t worry about the sig figs of conversion factors …
Because conversion factors are considered exact or defined (rather than measured) we don’t have to consider them for sig figs. Counted numbers also produce conversion factors of unlimited precision, which means there is no uncertainty in that factor.

42. Law of Conservation of Mass

43. Scientific notation
This is when we deal with really small numbers or really big numbers. Written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.

44. Scientific Notation 602 200 000 000 000 000 000 000 atoms
5280 = 5.28 x = 8.21 x 10 -2
For really big numbers and really small numbers.
Is used for really, really big numbers and really small numbers.
Add this: Look at the power of positive is for numbers greater than 1 and negative is for numbers less than 1.

45. Write 65 000 km in scientific notation, and show 2 sig figs.
6.5 x 10 4 km This shows 2 sig figs. What if I needed 3 sig figs? 6.50 x 10 4 km

46. Let’s write these in Scientific Notationm
46000 cows
112 pm
0.760 µg

47. When numbers are written in scientific notation, only the sig figs are shown.
Suppose you are expressing a very small quantity, such as the length of a flu virus. In ordinary notation this length could be mm. In scientific notation it would be 1.2 x mm

48. Determine M by moving the decimal in the original number to the left or right, so that only the nonzero digit remains to the left of the decimal. Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it right, n is negative.

49. Calculator time…

50. Calculations and Scientific Notation
(2.3 x 107) x (5.2 x 10-4) 2.3 x x 10-4 (8.99 x 10-4 m) x ( 3.57 x 104 m) =

51. Sample F, Pg. 52
Calculate the volume of a sample of aluminum that has a mass of kg. The density of aluminum is 2.70 g/cm3. V = kg x 1000 g = … cm g/cm3 1 kg How many sig figs do we need?
D = m/v / 2.70 g/cm3

52. Right! We need 3
V = 1.13 x 103 cm3

53. Let’s Practice: Pg. 52
Practice Problems: 1 – 3 Wanna really stretch your brain: try #4!

55. Target 9/8
Polycarbonate plastic has a density of 1.2 g/cm3. A photo frame is constructed from two 3.0 mm sheets of polycarbonate. Each sheet measures 28 cm by 22 cm. What is the mass of the photo frame?
1.2 g/cm3 = mass/ v (28 x 22 x .60 cm) …. 3.mm + 3.mm = 6 mm = .6 cm
M = 440 g

56. Target Qs How many sig figs are in each underlined measurement?
47.70 g of Cu
m of gold chain
Round each to 3 sig figs: L cg mL
4, 3
98.5 L, 7.63 x cg, 1.76 x 10 3 or 1760 mL

57. Homework

58. Significant Figures
We’ll consider the following to have an infinite number
of significant figures:
Counters – 30 eggs
Defined units – 12 inches = 1 foot
Significant figures and constants; use the number of
significant figures reported with the constant
X 108 m/s
3.00 x 108 m/s

59. Direct Proportions Page 53…
Two quantities are directly proportional to each other if dividing one by the other gives a constant value:
y = k The ratio between the variables
x remains constant.
Also written as y = kx
And when you graph y = kx, you get the straight line. Or a linear plot that passes through the origin results.

60. Direct Proportion Section 3 Using Scientific Measurements Chapter 2
Example: if the masses and volumes of different samles of Al are measured, the masses and volumes will be directly proportional to each other. As the mas increases, the volume increases by the same factor, as you can see from the data table. Doubling the mass doubles the volume. Halving the mass halves the volume.
Consider mass to be y and volume to be x. K would be the density. And the slope of the line relfects the constant density, or mass-volume ratio.

61. Inverse proportions
Two quantities are inversely proportional to each other if one decreases when the other increases.
Think of speed and time to cover a distance:
The greater the speed, the less time it takes. The less speed, the more time it takes.
Y ∞ 1/x . “y is proportional to 1 divided by x”
XY = K “ If x increases, y must decrease by the same factor to keep the product constant.

62. Inverse Proportion Section 3 Using Scientific Measurements Chapter 2
This graph shows an inversely proportional relationship. The curve is called a hyperbola.
When the temp of a sample of N is kept constant, the V of the gas decreases as the P incrases.
P and V are inversely proportional.

63. Time to think!
What would happen to the volume (or size) of the balloon if it was taken from a cool, AC’d building out into a hot, muggy summer day?
What does that tell you about volume and temperature?
Show the inflated balloon with the tied neck The volume would increase. They are directly proportional – they both increased.

64. Keep thinking…
What would happen to the volume of the balloon if someone gently sat on it?
Sitting on a balloon also changes its pressure.
How does the pressure change?
Are volume and temperature directly or inversely proportional?
Volume decreases if someone sits on it. The pressure increases.
They are inversely proportional: as the volume decrases the pressure increases.

65. See Saw Rule and Proportions
Whne one goes up, the toehr has to go down. Each person’s position is always the inverse or opposite of the other person’s.
When you have to decie direct or inverse, if you increase the value of one by doubling it, does the other variable double as well – that end of the see saw goes up – or does it decrease by half. (It decrases by half) .

66. Check!
Suppose you measure the classroom once using a piece of rope you know to be 10 m long and again with a tape marked in m, cm and mm. You then take the average of the two measurements. Which would determine the number of sig figs in your answer…
The measurement made with the rope would determine the number of sig figs b/c the rope is not marked with smaller units. It cannot measure as accurately. The least accurate measurement – the one made using the rope – determines the number of sig figs in the answer.

67. Answer:
The least accurate measurement – the one made using the rope – determines the number of sig figs in the answer.
The rope isn’t marked with smaller units so it can’t measure as accurately.