Sig Figs

Report
Chapter 2: Measurement and Calculations
Key concepts:
 Differentiate between accuracy and precision
Apply principles of measurement and
significant figures
 Identify and use the 7 base SI units
 Name and apply units of measure
 Perform unit conversions
 Calculate density
 Calculate percent error
A. Accuracy vs. Precision
ACCURACY - How close you are to the correct
__________
measurement or calculation based on the
standard value.
PRECISION - How close your measurements are to
__________
EACH OTHER
The density of aluminum is 2.78 g/cm3.
Bob calculates the density three times and gets 2.75, 2.79 and 2.77.
AVG: 2.77
ACCURATE AND PRECISE
Mary calculates the density three times and gets 4.66, 4.67, and 4.65
AVG: 4.66
PRECISE BUT NOT ACCURATE
Holden calculates the density three times and gets 10.25, 6.87, and 1.25
AVG: 6.12
NIETHER ACCURATE NOR PRECISE
Franz calculates the density three times and gets 2.90, 1.95, 3.44
AVG: 2.76
ACCURATE BUT NOT PRECISE
B. Measurement
Measurement Something with magnitude, size or
___________
amount.
Unit
________
- Compares what is measured to a
defined size.
Metric - Standard system of measure using
________
base 10.
SI
________
- The international system of measure
that uses only BASE metric units
B. Measurement
Quantitative - Measurements having numbers or
___________
size.
Qualitative - Measurement having subjective
___________
descriptions
Examples:
20 ml of water
QUANTITATIVE
The reaction bubbles
QUALITATIVE
Uma Thurman is blonde
QUALITATIVE
17 g/ml
QUANTITATIVE
Bulldogs are #1
QUALITATIVE
C. Significant figures
Significant figures indicate the accuracy of the
measuring instrument.
2.35 cm
Last digit is ESTIMATED
Not possible to estimate 2.3514584;
can only estimate between graduations
C. Significant figures
Consider the following:
What’s the estimate?
This ruler isn’t as accurate as the previous.
C. Significant figures
RULE
EXAMPLE
All nonzero digits and
zeros between those digits
are significant
1 458 g
Leading zeros with decimal
points are NOT significant;
Ending zeros ARE
significant with decimal
0.0005 kg
Ending zeros left of the
decimal point may or may
not be significant.
Indication needed.
15 000 kg
40.7 m
10 150.01 mm
0.01008 m
1 701.10 L
0.00140500 m
15 000. kg
1.50E4 kg
1.500E4 kg
NO. OF SIG FIGS
4
3
7
1
4
6
6
2
5
3
4
Scientific notation is always in sig fig form
C. Significant figures
ADDITION AND SUBTRACTION
Answer has as many DECIMAL POINTS
as the part with the LEAST decimals.
5.44 – 2.6106 = 2.8294
2.83
-13.4
2.4 – 15.82 = -13.42
2.099 + 0.05681 = 2.15581
2.156
0.258 + .1 = 0.358
0.4
C. Significant figures
MULTIPLICATION AND DIVISION
Answer can only contain as many SIG FIGS
as the part with the LEAST sig figs
8.15 x 6 = 50
48.9
0.250 / 0.87 = 0.29
0.2873563218
1.2 x 1010 = 1200
1212
17.05 / 1.50 = 11.4
11.3666666666
C. Significant figures
How about this one: (not in your notes; use calc)
1.2  0.34

0.601  0.5
20
D. SI base units
Quantity
Unit
Abb.
Length
Mass
Meter
m
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
Amount of substance
E. Current
Mole
Ampere
mol
Luminous intensity
candela
cd
Scientific researchers
use ONLY these units!
A
We
won’t
D. SI Base units cont.
Derived units – Made up of the base units
Quantity
SI Unit
Other Units
Area
m2
acres, cm2, ft2
Volume
m3
L, gal, cm3
Density
kg
g
m
3
Speed
m
Energy
kg  m2
cm3
slugs
ft3
mi/hr, ft/s
s
s
2
Calorie, kWhr
E. Unit Conversions – metric prefixes
kilo
hecto
deca
unit
deci
centi
milli
king
hector
Doesn't
Usually
Drink
Chocolate
milk
u  g,m,L, etc.
EXAMPLES
1 000g = ________ Kg
0.043 dam = _______ mm
0.23 Kg =________ dg
15.25 cL = ________ HL
345 DaL = _____ Km 101.34 Km = ___________ mm
F. Metric conversions – conversion factors
All conversions start with an EQUALITY
1 inch is the same as 2.54 cm
1 inch = 2.54 cm
Equalities are turned into conversion factors:
1inch
2.54cm
or
2.54cm
1inch
Notice the
top and
bottom are
same length!
F. Metric conversions – conversion factors
Convert 34 inches to centimeters
34 in



2.54 cm
1 in



Conversion factor
goes here
86.36 cm
F. Metric conversions – conversion factors
The Bulldogs need 550 cm for a first down. How
MULTImany yards is that?
STEP
Plan: cm  inch  feet  yards
yd 





in
1
ft
1
1
550 cm 
 6 yards





 2.54 cm  12 in   3 ft 
F. Metric conversions – conversion factors
A baseball is thrown 60 ft/s. How fast is this in
Two things
miles/hour?
to convert.
Do one at
1. ft  miles
a time.
2. s  min  hours
ft 
1 mi
60 
s  5280 ft
  60 s   60 min 
 40.91 mi/hr




1 hr 
  1 min  
F. Metric conversions – powered units
Misconception: 1 m = 100 cm but
1m3 ≠ 100 cm3
1 m3 cube
1m
100 cm
1m
100 cm
1m
100 cm
So, 100x100x100 =
1,000,000 cm3
If the unit is cubed,
you cube the numbers
too
(1 m)3 = (100 cm)3
1 m3 = 1,000,000 cm3
F. Metric conversions – Volumes
Critical equality:
1 ml = 1 cm3
How many liters of fuel does a 300 m3 tank hold?
3 
cm
1,000,000


3
300 m 

3
1
m 

1 ml  1 L  
300,000
L



3
1 cm  1,000 ml
Or you could do King Hector
F. Metric conversions - Temperature
180 Fo = ? K
Thou shalt use:
Work:
F  C  32
o
F  32
o
C 
9
o
9
5
o
5
C  82.2
o
K  C  273
o
o
F  C  32
o
9
5
K  C o  273
K  355K
o
G. Density
Measure of how tightly packed matter is.
More dense
Floating Boat on SF6
Inhaling SF6
G. Density, cont.
mass
m
D

volume V
g
g
or
Units:
3
cm
ml
When measuring
LxWxH
When measuring
Volume w/ cylinder
G. Density, cont.
A 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:
m
V
D
25g
V
.87 g/ml
V  28.74ml
V  29ml(sigfigs)
H. Percent Error
Va  Ve
%E 
Va
%E = Percent error
Va = Accepted value
Ve = Experimental value
Example:
A student measures the density of a solid as
3.42 g/cc. The solid really has a density of 3.76
g/cc. Calculate the percent error. cc = cubic
centimeter
Va = 3.76 g/cc
Ve = 3.42 g/cc
H. Percent Error, cont
Given:
Work:
Va = 3.76 g/cc
Ve = 3.42 g/cc
Va  Ve
%E 
Va
Watch
parentheses
here!!!
3.76  3.42
%E 
3.76
%E = 0.09042
%E = 9.04% (sig figs)
You can ignore negative signs. A positive
percent means the accepted value is higher
than your value. A negative means it’s
lower.

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