Unit 2.
Measurement
Do Now
 In
your own words, what do you think is the
difference between:

Accuracy and Precision?
A. Accuracy vs. Precision
 Accuracy
- how close a measurement is to the
accepted value
 Precision
- how close a series of measurements are
to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
ACCURATE = CORRECT
PRECISE = CONSISTENT
B. Percent Error

Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
 100
B. Percent Error

A student determines the density of a substance to be
1.40 g/mL. Find the % error if the accepted value of
the density is 1.36 g/mL.
% error 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.90 %
 100
C. Significant Figures
 Indicate
precision of a measurement.
 Recording

Sig Figs
Sig figs in a measurement include the known digits
plus a final estimated digit
C. Significant Figures
 Indicate
precision of a measurement.
 Recording

Sig Figs
Sig figs in a measurement include the known digits
plus a final estimated digit
2.35 cm
C. Significant Figures

Counting Sig Figs (Table 2-5, p.47)
 Count
all numbers EXCEPT:
Leading
zeros -- 0.0025 (not significant)
Trailing
zeros without a decimal point -2,500 (not Significant)
Zeros
between numbers are significant
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
C. Significant Figures
 Calculating

with Sig Figs
Multiply/Divide –
The # with the fewest sig figs determines the #
of sig figs in the answer.
Multiplication and Division
Rules
 Do
the sum
 Round the answer to the least significant
figure in the problem
 13.91g/cm3)(23.3cm3)
4SF
3SF
= 324.103g
3SF
324g
C. Significant Figures
 Calculating

with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value
determines the place of the last sig fig in the answer.
Addition and Subtraction
Rules
 Stack
the numbers so that the decimal
point is aligned
 Do the sum
 Figure out which number has least
decimal place (least precise/decimal
area least far out)
 Draw a line after the last number with the
least decimal place
 Round the digit by looking at the number
that follows
Example
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
C. Significant Figures
 Calculating

with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the
answer.
 Counting
 Exact
 “1”
numbers: 12 students
conversions: 1 m = 100 cm
in any conversion: 1 in = 2.54 cm
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL
 2.4 g/mL
2 SF
6.
18.9 g
- 0.84 g
18.06 g
 18.1 g
D. Scientific Notation
65,000 kg  6.5 × 104 kg
 Converting
into Sci. Notation:

Move decimal until there’s 1 digit to its left.
Places moved = exponent.

Large # (>1)  positive exponent
Small # (<1)  negative exponent

Only include sig figs.
D. Scientific Notation
Practice Problems
7. 2,400,000 g
8. 0.00256 kg
9.
7  10-5 km
10.
6.2  104 mm
D. Scientific Notation
Practice Problems
7. 2,400,000 g
2.4  106 g
8. 0.00256 kg
2.56  10-3 kg
9.
7  10-5 km
0.00007 km
10.
6.2  104 mm
62,000 mm
D. Scientific Notation
 Calculating
with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
E. Proportions
 Direct
Proportion
y x
 Inverse
y
x
Proportion
1
y
x
y
x
Units of
Measurement
 Quantity
- number + unit
A. Number vs. Quantity
UNITS MATTER!!
B. SI Units
Quantity
Symbol
Base Unit
Abbrev.
Length
l
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temp
T
kelvin
K
Amount
n
mole
mol
B. SI Units
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
C. Derived Units
 Combination
 Volume

of base units.
(m3 or cm3)
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
 Density
 (kg/m3 or g/mL or g/cm3)
mass per volume
M
D=
V
D. Density
Mass (g)
Δy M
D

slope 
Δx V
Volume (cm3)
Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
D. Density
 An
object has a volume of 825 cm3 and a density of 13.6
g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M=?
M
D
V
WORK:
D. Density
 An
object has a volume of 825 cm3 and a density of 13.6
g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
M=?
M = DV
M
D
V
M = (13.6
g/cm3)(825cm3)
M = 11,200 g
A
D. Density
liquid has a density of 0.87 g/mL. What volume is
occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V=?
M = 25 g
M
D
V
WORK:
A
D. Density
liquid has a density of 0.87 g/mL. What volume is
occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
M = 25 g
V=M
D
M
D
V
V=
25 g
0.87 g/mL
V = 29 mL
III. Unit Conversions
A. SI Prefix Conversions
1.
Find the difference between the exponents of the
two prefixes.
2.
Move the decimal that many places.
To the left
or right?
A. SI Prefix Conversions
move right
move left
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
A. SI Prefix Conversions
1) 20 cm =
______________ m
2) 0.032 L = _____________ mL
3) 45 m =
______________ nm
4) 805 dm = ______________ km
A. SI Prefix Conversions
0.2
1) 20 cm = ______________
m
32
2) 0.032 L = ______________
mL
3) 45 m =
45,000
______________
nm
0.0805
4) 805 dm = ______________
km
C. Johannesson
B. Dimensional Analysis
 The

“Factor-Label” Method
Units, or “labels” are canceled, or “factored” out
g
cm 

g
3
cm
3
B. Dimensional Analysis
 Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by
bottom number.
4. Check units & answer.
B. Dimensional Analysis
 Lining
 ARE
up conversion factors:
THESE THE SAME?
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
B. Dimensional Analysis
 How
many milliliters are in 1.00 quart of milk?
qt
mL
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
B. Dimensional Analysis
 You
have 1.5 pounds of gold. Find its volume in cm3 if
the density of gold is 19.3 g/cm3.
cm3
lb
1.5 lb 1 kg 1000 g 1 cm3
2.2 lb
1 kg
19.3 g
= 35 cm3
B. Dimensional Analysis
 How
many liters of water would fill a container that
measures 75.0 in3?
in3
75.0 in3 (2.54 cm)3
(1 in)3
1L
1000 cm3
L
= 1.23 L
B. Dimensional Analysis
5) Your European hairdresser wants to cut your hair 8.0
cm shorter. How many inches will he be cutting off?
cm
in
8.0 cm 1 in
2.54 cm
= 3.2 in
B. Dimensional Analysis
6) Taft football needs 550 cm for a 1st down. How
many yards is this?
cm
550 cm
yd
1 in
1 ft 1 yd
2.54 cm 12 in 3 ft
= 6.0 yd
B. Dimensional Analysis
7) A piece of wire is 1.3 m long. How many 1.5-cm
pieces can be cut from this wire?
cm
pieces
1.3 m 100 cm
1m
1 piece
1.5 cm
= 86 pieces