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Chapter 1
Understanding the Math in Chemistry
I.
What are significant figures/digits?
A.
Significant figures (digits) are a combination of
certain as well as uncertain numbers.
B.
Example:
48.3
Estimated
Certain
value
48.2896 (rounded up)
48.3101 (rounded down)
This is the way I learned the sig. fig. rules
1. Any digit that is not zero is significant. 1234.56 6 significant figures
1234.56 6 significant figures
2. Zeros between non-zero digits are significant.
1002.5 5 significant figures
3. Zeros to the left of the first non-zero digit are not significant.
000456 3 significant figures 0.0056 2 significant figures
4. If the number is greater than one (1), then all zeros to the right of the decimal
point are significant.
457.12 5 significant figures 400.00 5 significant figures
5. If the number is less than one, then only zeros that are at the end of the
number and between non-zero digits are significant.
0.01020 4 significant figures
6. For numbers that do not contain decimal points, the trailing zeros may or may
not be significant. In this course assume the digits are significant unless told
otherwise.
1000 1, 2, 3, or 4 significant figures. UNCLEAR assume 4 in calculation 0.0010
2 significant figures 1.000 4 significant figures
7. Assume defined and counted quantities have an unlimited number of
significant figures.
This will not be the way I teach it to you!!
Here are two simple rules!!
Know them!
C.
Significant Figures RULES
Rule #1:
Rule #2:
If a decimal point is present count from
Left to Right (L R) DO NOT START WITH 0
If a decimal point is absent count from
Right to Left (L R) DO NOT START WITH 0
D.
Predict the amount of sig. figs in the following:
1.
138.7
2.
100
3.
0.00320
4.
0.0050
5.
89.0
6.
890
7.
0.0030
8.
1000
4 sig. figs.
1 sig. fig.
3 sig. figs.
2 sig. figs.
3 sig. figs.
2 sig. figs.
2 sig. figs.
1 sig. fig.
9.
1000.
10.
10500
4 sig. figs.
3 sig. figs.
II. Scientific Notation
A.
General Equation:
Examples:
1≤ M <10
Is this an
acceptable M?
Answer: 1.387 X 10 2
1.
138.7
.
How many places do you have to move the
decimal to get to an acceptable M?
2.
100
Answer: 1 X 10 2
3.
M X 10n
0.000320
Answer: 3.20 X 10 -4
n= the number of
decimal places moved
to get to an acceptable
M value
+n= greater than 1
-n = less than 1
# of sig. figs in value must match the # of sig figs in
scientific notaion
B. On your own:
4.
5.
6.
0.0050
89.0
890
Answer: 5.0 X 10 -3
Answer: 8.90 X 101
Answer: 8.9 X 10 2
Answer: 3. 0 X 10 -3
7.
0.0030
8.
1000
Answer: 1 X 10 3
9.
1000.
Answer: 1.000 X 103
10.
10500
Answer: 1.05 X 104
C. Going backwards
1.50 X 10
3.5 X 10
2
-4
Move decimal point to
make it larger than 1
Move decimal point to
make it smaller than 1
150.
.00035
Warm up 9/6
Are these equal? If they are, write yes, if not,
correct the “regular” value.
1.
2.
3.
4.
2.5 X 10-4 = .000025
9.91 X 102= 991
4.500 X 103= 4500
5.700 X 10 -3= .057
Incorrect: .00025
Correct
Incorrect: 4500.
Incorrect: .005700
Rounding Rules
III.
Adding and Subtracting Rounding Rules
The answer must contain as many decimal places
as the least accurate value (the one with the least #
of decimal places)
1. 122.5 L.a
2. 101
52.68
+
2.11
177.29
177.3
+
3.
4.
6.8
86.232
3.17
- 5.00_____
110.97
111
122.4
0.05
+ 1.000
123.45
81.232
81.23
123.4
123.5
If you stand on the scale and it says: 122.5lbs?
Would it be fair to say 123???
I don’t think so!!
Why do you always round up??
IV. ODD/EVEN Rule is used
when only a 5 is next to the digit you
are interested in rounding……
ODD Digit Round up
Even Digit Leave it alone
(EVEN…LEAVIN!!)
Let’s practice rounding to 3 sigs figs.
1.
2.
107.5=
112.5=
108
112
1.16
3.
1.155
4.
9.8451=
9.85
5.
854.54=
855
6.
.02545=
.0254
V. Multiplication and Division Rules
The answer must contain as
many significant figures as
the value with the least
number of significant figures
Examples:
3
4
1.
35.72 (0.00590)=
5
2.
3.
4.
3
4450/ 5.00=
4
.211
2
6810.2/2.4 =
3
.210748
2837.58333
2800
How many sig figs?
890
890.
3
.3287 (45.2)=
14.85724
14.9
d.
Mixture
Homogeneous Mixture:
Visible components are
all similar
Heterogeneous Mixture:
Has visible distinction
between parts
VII. Changes in Matter can be
physical or chemical
A.
Physical change:
Identity of substance
is NOT altered.
B.
Chemical change:
New substance has
different set of
properties.
Changes in Matter Video clip
DENSITY
may affect your
DESTINY!
Is it a compliment if someone
says……You’re DENSE!
According to your
understanding….
What’s more dense?
A Rock
or
A Sponge
Ice Cubes or Liquid Water
Ice (H2O(s))
Liquid water
(H2O(l))
Water
expands
11%
when it
freezes
Oil 
Adding
water
based
food
coloring
Water
Which one is more dense??
WWF Wrestler
Sumu Wrestler
Coke v. Diet Coke
So what’s the difference between
accuracy and precision?
Accuracy refers to how closely a measured value agrees with the correct value.
Precision refers to how closely individual measurements agree with each other.
The repeatability of the results.
accurate
(the average is accurate)
not precise
precise
not accurate
accurate
and
precise
Definition for Density
• The amount of matter in a certain amount of
space (volume)
Equation for Density
D=Mass (g)
Volume (ml) or (cm3)