1. 8/29/11 1. Room Map 2. Tally Skills Test
3. E-2 Significant figures notes
4. E-2 Practice Problems

2. Significant Figures
As you learned in the measurement activity, an appropriate measurement for the length of the rectangle below is 3.65 cm. Because the “3” and the “6” are certain, and the “5” is our guess, all three digits are intentional or “significant.” Thus 3.65 cm contains three significant figures. 1 2 3 4 5 cm

3. Significant Figures
The scale below is less precise, and so the rectangle’s length should be reported as just 3.5 cm. This measurement has just two significant figures: the “3” and the “5” and it is considered to be a weaker, less valuable measurement than 3.65 cm. 1 2 3 4 5 cm

4. Significant Figures
The scale below, however, is more precise, and a magnified view (shown at right) is helpful in making a good reading: cm. This measurement has 4 significant figures: the “3.66…” which are certain, and the “5” which is the guess.
(3.6)
(3.7) 1 2 3 4 5 cm

5. Significant Figures 3.5 cm has two significant figures,
3.65 cm has three significant figures,
3.665 cm has four significant figures.
You might start to think that the number of significant figures is simply equal to the number of digits there are in a measurement, but that is not always the case…

6. Significant Figures
Consider the length of the rectangle below: mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant?
1000
2000
3000
4000
5000 mm

7. Significant Figures
Consider the length of the rectangle below: mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant?
NO! They are not considered significant.
1000
2000
3000
4000
5000 mm

8. Significant Figures
In 3500 mm, the zeroes are serving a very different purpose than the “3” and the “5.” These two zeroes are acting as place-keepers. They show the size of the measurement mm, not just 35 mm – but they do not make the measurement any more precise.
1000
2000
3000
4000
5000 mm

9. Thus 3500 mm has just two significant figures, not four.
1000
2000
3000
4000
5000 mm

10. Significant Figures
Now consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.)
1000
2000
3000
4000
5000 mm

11. Significant Figures
Now consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.)
If you said three, you are correct!
1000
2000
3000
4000
5000 mm

12. Significant Figures
In 3450 mm, the “3” and “4” are definite and the “5” is the guess, so those are the three significant figures. The zero at the end is a place-keeping zero, and so it is not considered to be significant.
1000
2000
3000
4000
5000 mm

13. Significant Figures
Now what about the measurement below: m? How many significant figures do you think it has? (Make a guess before continuing.)
0.001
0.002
0.003
0.004
0.005 m

14. Significant Figures
Now what about the measurement below: m? How many significant figures do you think it has? (Make a guess before continuing.)
If you said three, good job.
0.001
0.002
0.003
0.004
0.005 m

15. Significant Figures
In m, the “2” and “7” are definite and the “5” is the guess. Here the zeroes in the beginning of the number are place keepers. They make a small number, just as the zeroes in 3500 make it a big number.
0.001
0.002
0.003
0.004
0.005 m

16. Significant Figures
If you are good at converting numbers into scientific notation then this will help:

17. Significant Figures
If you are good at converting numbers into scientific notation then this will help:
170,000,000,000 converts into 1.7 x 1011.

18. Significant Figures
If you are good at converting numbers into scientific notation then this will help:
170,000,000,000 converts into 1.7 x 1011.
And converts into 5.63 x 10-6.

19. Significant Figures
If you are good at converting numbers into scientific notation then this will help:
170,000,000,000 converts into 1.7 x 1011.
And converts into 5.63 x Notice how scientific notation separates out all the significant figures and puts them in the beginning…
1.7 x x 10-6

20. Significant Figures
If you are good at converting numbers into scientific notation then this will help:
170,000,000,000 converts into 1.7 x 1011.
And converts into 5.63 x Notice how scientific notation separates out all the significant figures and puts them in the beginning…and it changes all the place-
keeping zeroes into a power of ten
1.7 x x 10-6

21. Significant Figures 3500 has two significant figures,
has three significant figures.
You might start to think that zeroes are never significant, but that is not always the case…

22. Consider the measurement shown below: 30.5 cm.
Significant Figures
Consider the measurement shown below:
30.5 cm. 10 20 30 40 50 cm

23. Significant Figures Consider the measurement shown below:
30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “5” is the guess. 10 20 30 40 50 cm

24. Significant Figures Consider the measurement shown below:
30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “6” is the guess.
30.5 cm has three significant figures. 10 20 30 40 50 cm

25. And consider the measurement shown below: 23.0 cm.
Significant Figures
And consider the measurement shown below:
23.0 cm. 10 20 30 40 50 cm

26. Significant Figures And consider the measurement shown below:
23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess. 10 20 30 40 50 cm

27. Significant Figures And consider the measurement shown below:
23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess.
23.0 cm has three significant figures. 10 20 30 40 50 cm

28. Rules for identifying significant figures in a measurement:
Rules recap thusfar:
Rules for identifying significant figures in a measurement:
All non-zero digits are significant (i.e. 1-9).
2. All zeros or groups of zeros between non zero digits
are significant (ex. ALL the zeros in 703 g, mL, and cm are
all significant because of rule #2a.)
AND all zeros between a non-zero digit on the left and
a decimal on the right are also significant (ex. ALL the zeros in
140. cm, mL, are g are all significant because of rule #2b.).
These 2 types of zeros can be referred to as “squeezed zeros.”
3. All zeros or groups of zeros to the right of the decimal AND
at the end of the number are significant (ex. ALL the zeros in
2.30 cm, 7.00 mL, and g are all significant because of rule #3.).
These zeros can be referred to as “trailing zeros.”
**ALL other types of zeros are NOT significant and serve only
as place holders (ex. The zeros in 300 cm and mL ARE NOT significant
since they are neither “squeezed zeros” nor “trailing zeros”).
Remember, significant means measured, not important
(Place holder zeros ARE still important even if they aren’t significant!)!

29. If the decimal point is Absent, count from the Atlantic.
All those rules seem a bit tough to keep straight?
While you should remember why we do sig figs,
and what makes something “significant,”
here’s a handy trick to help you count your sig figs:
If the decimal point is Absent, count from the Atlantic.
If the decimal point is Present, count from the Pacific.
________________________________________________________________
For example: has no decimal point. The Altantic rule applies!
|<---- starting from the “Atlantic,” heading “west,”
the first non-zero digit we hit is the 2, and everything after that is also significant. So has 4 significant figures!

31. SHORTCUT! HANDY TRICK!
If the decimal point is Absent, count from the Atlantic.
If the decimal point is Present, count from the Pacific.

32. We’ll stop here for Day 1 of E2
Day 1 Homework:
Bottom of page 10 in WB
#1 ALL,
#2 a-h
Want more practice? Keep going on these slides from the blog (MHSchemistry.wordpress.com)!
There’s a good recap at slide #130, just before Day 2 notes pick up.

33. Significant Figures
Now, let’s see how much you have learned about significant figures.
What follows are 50 different problems. For each one, simply think of the how many significant figures there are, then go to the next slide to see if you are correct. If you are correct, go on to the next problem. If not, try to figure out why your answer is incorrect.

34. Significant Figures
34.84 cm

35. Significant Figures
34.84 cm
4 sig figs

36. Significant Figures
63 g

37. Significant Figures
63 g
2 sig figs

38. Significant Figures
109 m

39. Significant Figures
109 m
3 sig figs

40. Significant Figures
17.03 cm

41. Significant Figures
17.03 cm
4 sig figs

42. Significant Figures
290 mm

43. Significant Figures
290 mm
2 sig figs

44. Significant Figures s

45. Significant Figures s
2 sig figs

46. Significant Figures kg

47. Significant Figures kg
3 sig figs

48. Significant Figures
70400 mL

49. Significant Figures
70400 mL
3 sig figs

50. Significant Figures L

51. Significant Figures L
4 sig figs

52. Significant Figures
33.0 J

53. Significant Figures
33.0 J
3 sig figs

54. Significant Figures cm

55. Significant Figures cm
5 sig figs

56. Significant Figures
600 mg

57. Significant Figures
600 mg
1 sig fig

58. Significant Figures m2

59. Significant Figures m2
5 sig figs

60. Significant Figures s

61. Significant Figures s
2 sig figs

62. Significant Figures
55 mi/hr

63. Significant Figures
55 mi/hr
2 sig figs

64. Significant Figures
5.62 x 107 mm

65. Significant Figures
5.62 x 107 mm
3 sig figs

66. Significant Figures
8 x 10-4 g

67. Significant Figures
8 x 10-4 g
1 sig fig

68. Significant Figures
3.0 x 1014 atoms

69. Significant Figures
3.0 x 1014 atoms
2 sig figs

70. Significant Figures L

71. Significant Figures L
4 sig figs

72. Significant Figures
4050 g

73. Significant Figures
4050 g
3 sig figs

74. Significant Figures
g/mL

75. Significant Figures
g/mL
3 sig figs

76. Significant Figures
41,000 mm

77. Significant Figures
41,000 mm
2 sig figs

78. Significant Figures
25.0 oC

79. Significant Figures
25.0 oC
3 sig figs

80. Significant Figures
3.00 x 104 ms

81. Significant Figures
3.00 x 104 ms
3 sig figs

82. Significant Figures
5 x 10-7 K

83. Significant Figures
5 x 10-7 K
1 sig fig

84. Significant Figures L

85. Significant Figures L
3 sig figs

86. Significant Figures
30200 cm3

87. Significant Figures
30200 cm3
3 sig figs

88. Significant Figures
210.4 cg

89. Significant Figures
210.4 cg
4 sig figs

90. Significant Figures
340 km

91. Significant Figures
340 km
2 sig figs

92. Significant Figures
340.0 km

93. Significant Figures
340.0 km
4 sig figs

94. Significant Figures
0.500 Hz

95. Significant Figures
0.500 Hz
3 sig figs

96. Significant Figures m

97. Significant Figures m
5 sig figs

98. Significant Figures
50,400 m

99. Significant Figures
50,400 m
3 sig figs

100. Significant Figures
23,000 cm

101. Significant Figures
23,000 cm
2 sig figs

102. Significant Figures cm

103. Significant Figures cm
5 sig figs

104. Significant Figures
1,000,000 mi

105. Significant Figures
1,000,000 mi
1 sig fig

106. Significant Figures
1,000,001 mi

107. Significant Figures
1,000,001 mi
7 sig figs

108. Significant Figures
0.30 mL

109. Significant Figures
0.30 mL
2 sig figs

110. Significant Figures
4.00 x 103 g

111. Significant Figures
4.00 x 103 g
3 sig figs

112. Significant Figures s

113. Significant Figures s
3 sig figs

114. Significant Figures
530 m

115. Significant Figures
530 m
2 sig figs

116. Significant Figures
7 km

117. Significant Figures
7 km
1 sig fig

118. Significant Figures
400 kg

119. Significant Figures
400 kg
1 sig fig

120. Significant Figures m3

121. Significant Figures m3
2 sig figs

122. Significant Figures
7060 g/L

123. Significant Figures
7060 g/L
3 sig figs

124. Significant Figures
So… How did you do? With more practice, you should be able to zip through those problems with no mistakes!

125. Significant Figures
Although you have not been given any specific rules about whether or not a digit in a number is significant or not, see if you can figure out those rules for yourself:
(write your list of rules in your notebook.)

126. Significant Figures
Although you have not been given any specific rules about whether or not a digit in a number is significant or not, see if you can figure out those rules for yourself:
(write your list of rules in your notebook.)
For example, what about nonzero digits (like 2 or 7): when are they significant?

127. Significant Figures
Although you have not been given any specific rules about whether or not a digit in a number is significant or not, see if you can figure out those rules for yourself:
(write your list of rules in your notebook.)
For example, what about nonzero digits (like 2 or 7): when are they significant? And what about zeroes: when are they significant?

128. Significant Figures
When you have finished your list, make sure it covers all cases: zeroes in the beginning of numbers, in the middle and at the end… with decimal points and without…. with lines and without…scientific notation…

129. Significant Figures
When you have finished your list, make sure it covers all cases: zeroes in the beginning of numbers, in the middle and at the end… with decimal points and without…. with lines and without…scientific notation…
Then compare your set of rules to the ones that follow:

130. Significant Figures
Here is one way to represent the rules for significant figures:
Nonzero digits (26.3) are always significant.
(so 26.3 has three significant figures)
Zeroes occur in three different places in a number:
If they are at the beginning (0.005), they are never significant.
(so has one significant figures)
If they are in the middle (1207), they are always significant.
(so 1207 has four significant figures)
And if they are at the end, they are sometimes significant.
If there is a decimal point (21.600) they are significant.
(so has five significant figures)
If there is no decimal point (21600), they are not significant.
(so has three significant figures)

131. Significant Figures
The only exception to those rules is when there is a line over a zero (630000). When there is a line over a zero, treat that zero like a nonzero digit. So would have four significant figures. But Mrs. A won’t use this in Chem 1.
As for scientific notation (3.40 x 106), it follows these same rules if you just ignore the “times ten to the whatever power.” Or, simply put, every digit to the left of the times sign is automatically significant.
So 3.40 x 106 has three significant figures.

132. DAY 2 of E2 (sig figs) Remember that “significant” means “measured”.
We should always report our measurements as accurately as possible with the tools we are using. (Measure to the smallest mark the scale allows, then estimate one more decimal beyond).
We went over the rules yesterday, and I also shared a handy trick with you (the “Atlantic-Pacific Rule”):
If the decimal is If the decimal is
Present, count Absent, count
from the Pacific from the Atlantic.

133. Let’s go over the Practice Problems! Pg 10 in WB:
How many significant figures are in each of the following?
a cm e cm i cm
202 mL f mL j mL
0.202 g g g k g
200 kg h kg l x 103 kg

134. How many sig figs in the following? 365 m 42,000 L 1030 mm 0.414 cm
p. 10 #2 a-h
How many sig figs in the following?
365 m
42,000 L
1030 mm
0.414 cm m
42.0 L
6.4 x 103 mm
3.00 x 10-1 cm

135. What happens when we do math with our measurements?
So you’ve accurately measured in the lab and
reported with the correct sig figs… now what?
For example, let’s say you measured 2.35 g
pressing on an area of 6.70 cm2.
Calculate the pressure in grams per cm2;
2.35g ÷ 6.70 cm2
What does your calculator say?
Probably !
Did you measure to the millionths? No!
We need some more sig fig rules to save us from these runaway, misleading digits!

136. Sig Figs in Addition + Subtraction:
When adding or subtracting measurements,
determine which measurement has the fewest significant
PLACES (= your least precise measurement).
1062 m kg
m kg
1472 m = 1470 m kg = kg
After calculating, ROUND your answer to only as many
significant PLACES as that least precise measurement
that was used in the calculation.

138. Sig Figs in Multiplication & Division:
When multiplying or dividing measurements,
determine which measurement has the fewest TOTAL
significant figures (= your least precise measurement).
3 m x 102 m = 306 m2 = 300 m2
0.072 g ÷ mL = … g/mL = 0.67 g/mL
Don’t forget to round the last digit as needed
(if the first dropped digit is 5 or greater, round UP).
When calculating with labels, don’t forget to
add, subtract, multiply, or divide the labels, too!
(cm x cm = cm2) (g ÷ mL = g/mL)

140. HOMEWORK:
Look over Safety Notes (quiz tomorrow!)
Get Safety Contract signed
Don’t forget the Career Wksht is due Friday.
P.P. page 11 from WB due tomorrow.
Do these on a separate paper, not in WB!!!
#3: a & b
#4:
#5:
#6: