Transcript II. Units of Measurement - Fort Thomas Independent Schools

I. Scientific Method
The Scientific Method
A logical approach to solving
problems or answering questions.
Starts with observation- noting and
recording information and facts
hypothesis- educated guess or
testable statement
Steps in the Scientific Method
1. Observations (uses your senses)
a) quantitative involves numbers = 95oF
b) qualitative is word description = hot
2. Formulating hypotheses (ideas)
3. Performing experiments (the test)
- gathers new information to help
decide whether the hypothesis is valid
Scientific Method
 Controls- constants
 Variables- changing conditions
Limit variables
 We gather data and observations by
doing the experiment
 Modify hypothesis - repeat the cycle
based on results

Steps in the Scientific Method
 Theorize (model)
- explanation of some natural phenomenon
 Many phenomena- construct a theory
 Publish Results
- Do other experts agree
II. Units of Measurement
Number vs. Quantity
 Quantity - number + unit
UNITS MATTER!!
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
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
Derived Units
 Combination of base units.
 Volume
(m3
or cm3)
 length  length  length
 Density (kg/m3 or g/cm3)
mass per volume
1 cm3 = 1 mL
1 dm3 = 1 L
M
D=
V
Density
Mass (g)
Δy M
D

slope 
Δx V
Volume (cm3)
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
Density
 A 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. Using Measurements
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
Percent Error
 Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
 100
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 = 3 %
 100
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
Significant Figures
 Counting Sig Figs (Table 2-5, p.47)
 Count all numbers EXCEPT:

Leading zeros -- 0.0025

Trailing zeros without
a decimal point -- 2,500
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
Significant Figures
 Calculating with Sig Figs
 Multiply/Divide - The # with the fewest sig
figs determines the # of sig figs in the
answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
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.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
224 g
+ 130 g
354 g  350 g
Significant Figures
 Calculating with Sig Figs (con’t)
 Exact Numbers do not limit the # of sig
figs in the answer.
Counting numbers: 12 students
 Exact conversions: 1 m = 100 cm
 “1” in any conversion: 1 in = 2.54 cm

Significant Figures
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
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.
Scientific Notation
Practice Problems
7.
8.
9.
2,400,000 g
2.4 
0.00256 kg
2.56 
6
10
g
-3
10
kg
7  10-5 km 0.00007 km
10. 6.2  104 mm
62,000 mm
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
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Proportions
 Direct Proportion
y x
y
x
 Inverse Proportion
1
y
x
y
x
Unit Conversions
Dimensional Analysis
 The “Factor-Label” Method
 Units, or “labels” are canceled, or “factored”
out
g
cm 

g
3
cm
3
Dimensional Analysis
 Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units
cancel.
3. Multiply all top numbers & divide by
each bottom number.
4. Check units & answer.
Dimensional Analysis
 Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
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
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
Dimensional Analysis
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
Dimensional Analysis
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
Dimensional Analysis
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
SI Prefix Conversions
1) 20 cm =
0.2
______________
m
2) 0.032 L =
32
______________
mL
3) 45 m =
45,000
______________
nm
4) 805 dm =
0.0805
______________
km