chapter 2: measurement and calculations key concepts: differentiate between accuracy and precision ...
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Chapter 2: Measurement and Calculations
Key concepts: Differentiate between accuracy and precisionApply 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
Mary calculates the density three times and gets 4.66, 4.67, and 4.65
AVG: 4.66
Holden calculates the density three times and gets 10.25, 6.87, and 1.25
AVG: 6.12
Franz calculates the density three times and gets 2.90, 1.95, 3.44
AVG: 2.76
ACCURATE AND PRECISE
ACCURATE BUT NOT PRECISE
PRECISE BUT NOT ACCURATE
NIETHER ACCURATE NOR PRECISE
B. Measurement
___________ Something with magnitude, size or amount.
Measurement
________ - Compares what is measured to a defined size.
Unit
________ - The international system of measure that uses only BASE metric units
SI
________ - Standard system of measure using base 10.
Metric
B. Measurement
___________ - Measurements having numbers or size.
Quantitative
___________ - Measurement having subjective descriptions
Qualitative
Examples:20 ml of water
The reaction bubbles
Uma Thurman is blonde
17 g/ml
Bulldogs are #1
QUANTITATIVE
QUANTITATIVE
QUALITATIVE
QUALITATIVE
QUALITATIVE
C. Significant figures
Significant figures indicate the accuracy of themeasuring 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 figuresRULE EXAMPLE NO. OF SIG FIGS
All nonzero digits and zeros between those digits are significant
1 458 g
40.7 m
10 150.01 mm
Leading zeros with decimal points are NOT significant; Ending zeros ARE significant with decimal
0.0005 kg
0.01008 m 1 701.10 L
0.00140500 m
Ending zeros left of the decimal point may or may not be significant. Indication needed.
15 000 kg
15 000. kg
1.50E4 kg
1.500E4 kg
4371466
253
Scientific notation is always in sig fig form
4
C. Significant figures
ADDITION AND SUBTRACTION
Answer has as many DECIMAL POINTSas the part with the LEAST decimals.
5.44 – 2.6106 = 2.4 – 15.82 =
2.099 + 0.05681 = 0.258 + .1 =
2.82942.83 -13.42-13.4
2.155812.156 0.3580.4
C. Significant figures
MULTIPLICATION AND DIVISION
8.15 x 6 = 0.250 / 0.87 =
1.2 x 1010 = 17.05 / 1.50 =
48.9 0.2873563218
1212 11.3666666666
Answer can only contain as many SIG FIGSas the part with the LEAST sig figs
50 0.29
1200 11.4
C. Significant figures
How about this one: (not in your notes; use calc)
1.2 0.340.601 0.5
20
D. SI base units
Length Meter m
Mass Kilogram kg
Time Second s
Temperature Kelvin K
Amount of substance Mole mol
E. Current Ampere A
Luminous intensity
candela cd
Quantity Unit Abb.
Scientific researchersuse ONLY these units!
Wewon’t
D. SI Base units cont.
Derived units – Made up of the base units
Quantity SI Unit Other Units
Area
Volume
Density
Speed
Energy
m2
m3
3kg
m
ms
2
2kg m
s
acres, cm2, ft2
L, gal, cm3
3 3g slugs
cm f t
mi/hr, ft/s
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 2.54cmor
2.54cm 1inchNotice the
top andbottom are
same length!
F. Metric conversions – conversion factors
Convert 34 inches to centimeters
34 in in
cm
1
2.54
Conversion factorgoes here
86.36 cm
F. Metric conversions – conversion factors
The Bulldogs need 550 cm for a first down. Howmany yards is that?
550 cm
MULTI-STEP
Plan: cm inch feet yards
cmin
2.541
inft1
12 ft
yd13
6 yards
F. Metric conversions – conversion factorsA baseball is thrown 60 ft/s. How fast is this in miles/hour? Two things
to convert.Do one at
a time.
f t60
s ft
mi1
5280
smin1
60
minhr1
60 40.91 mi/hr
1. ft miles2. s min hours
F. Metric conversions – powered units
Misconception: 1 m = 100 cm but1m3 ≠ 100 cm3
1 m3 cube1 m
1 m
1 m100 cm
100 cm
100 cm
So, 100x100x100 =1,000,000 cm3
If the unit is cubed,you cube the numberstoo
(1 m)3 = (100 cm)3
1 m3 = 1,000,000 cm3
F. Metric conversions – Volumes
Critical equality:
How many liters of fuel does a 300 m3 tank hold?
300 m3 m3
cm3
11,000,000
cm3
ml
11
ml
L11,000 300,000 L
Or you could do King Hector
1 ml = 1 cm3
F. Metric conversions - Temperature
oK C 273 o o9
5F C 32
Thou shalt use:180 Fo = ? K
Work:
o o95F C 32
oo
95
F 32C
o oC 82.2oK C 273
K 355K
G. Density
Measure of how tightly packed matter is.
More dense
Floating Boat on SF6
Inhaling SF6
G. Density, cont.
mass mD
volume V
Units: 3
g gor
cm ml
When measuringLxWxH
When measuringVolume 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/mLV = ?M = 25 g
mD
V
Work:
mV
D
25gV
.87g/ ml
V 28.74mlV 29ml(sigfigs)
H. Percent Error
a e
a
V V%E
V
%E = Percent error
Va = Accepted value
Ve = Experimental value
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
Example:
H. Percent Error, cont
Given: Work:
Va = 3.76 g/ccVe = 3.42 g/cc
a e
a
V V%E
V
3.76 3.42
%E3.76
Watchparentheses
here!!!
You can ignore negative signs. A positive percent means the accepted value is higher than your value. A negative means it’s lower.
%E = 0.09042
%E = 9.04% (sig figs)