Transcript Measurements

Measurements
Measurements: Definitions
• Measurement:
– comparison between measured quantity and
accepted, defined standards (SI)
• Quantity:
– property that can be measured and described
by a pure number and a unit that names the
standard
Measurement
• Types:
– Qualitative:
• describe a substance without using numbers
(measurements).
– Quantitative:
• require measurement to be made and have to be
described by a QUANTITY (number and unit)
Measurement Requirements
• Know what to measure
• Have a definite agreed upon standard
• Know how to compare the standard to the
measured quantity (tool)
Types of measurement
• Quantitative– use numbers + units to describe the measured
quantity. Examples: the density of iron is 7.8 g/cm3.
• Qualitative– use description (language) without numbers to
describe the measurement
• Quantitative or qualitative?
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4 feet
extra large
Hot
100ºF
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Measuring
• Numbers without units are meaningless.
• The measuring instrument limits how good
the measurement is
Scientific Notations
• A shortcut method for writing very large and
very small numbers using powers of ten
• There should only be ONE digit in front of the
decimal.
602,000,000,000,000,000,000,000,000 = 6.02 x 10 23
• The number is written as M x 10n
if n is + number = large numbers (>0)
If n is - number = small numbers (<0)
Significant figures (sig figs)
• How many numbers while measuring are
important anything
• When we measure something, we can
(and do) always estimate between the
smallest marks.
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Significant Figures and
Measurement
• Measurement
– Done with tools
– The value depends on the smallest
subdivision on the measuring tool
• Significant Digits (Figures):
– consist of all the definitely known digits plus
one final digit that is estimated in between the
divisions.
Significant Figures (sig figs)
• The more marks give a better measured
value.
• Scientist always understand that the last
number measured is actually an estimate
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Sig Figs
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Only measurements have sig figs.
Counted numbers are exact
A dozen is exactly 12
A piece of paper is measured 11 inches
tall.
• Being able to locate, and count significant
figures is an important skill.
Significant Rules examples
• What is the smallest mark on the ruler that
measures 142.15 cm?
– ____________________
• 142 cm?
– ____________________
• 140 cm?
– ____________________
• Does the zero count?
• We need rules!!!
Easy way to remember Sig Fig
Rules
Pacific Ocean side of the US:
If there is a decimal point present
start counting from the left to right until
encountering the first nonzero digit and keep
counting
All digits thereafter are significant.
Atlantic Ocean side of the US:
If the decimal point is absent
start counting from the right to left until
encountering the first nonzero digit and keep
counting.
All digits thereafter are significant.
Sig figs.
How many SF in the following
measurements?
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2.
3.
4.
5.
6.
458 g
4085 g
4850 g
0.0485 g
0.004085 g
40.004085 g
Sig Figs.
7. 405.0 g
8. 4050 g
9. 0.450 g
10. 4050.05 g
11. 0.0500060 g
Rounding rules
Look at the number next to the one you’re
rounding.
0 - 4 : leave it
5 - 9 : round up
Round 45.462 to:
a) four sig figs
b) three sig figs
c) two sig figs
d) one sig fig
Calculations with Significant
Figures
Multiplication and Division
Same number of sig figs in the answer as
the least in the question
1) 3.6 x 653 = 2350.8
3.6 has 2 SF
653 has 3 SF
• answer can only have 2 SF
Answer: 2400
Multiplication and Division
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Same rules for division
practice
4.5 / 6.245
4.5 x 6.245
9.8764 x .043
3.876 / 1983
16547 / 714
Addition and Subtraction
While adding or subtracting, the answer is
reported to reflect the least precise # of sig
figs.
Add/Subtract the numbers together
Report the answer with the least # of sig figs
Ex. 1.2
+ 3.43 The answer will be 4.6
4.63
Practice
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4.8 + 6.8765
520 + 94.98
0.0045 + 2.113
6.0 x 102 - 3.8 x 103
5.4 - 3.28
6.7 - .542
500 -126
6.0 x 10-2 - 3.8 x 10-3
Accuracy, Precision, and
Certainty:
How good are the measurements?
Accuracy
how close the measurement is to the actual
value
Precision
how well can the measurement be repeated.
(How well do the measurements agree with
each other?)
Assessing Uncertainty
• The person doing the measuring should
asses the limits of the possible error in
measurement
Let’s use a golf anaolgy
Accurate? No
Precise? Yes
Accurate? Yes
Precise? Yes
Precise?
No
Accurate? Maybe?
Accurate? Yes
Precise? We cant say!
In terms of measurement
• Three students measure the
room to be 10.2 m, 10.3 m
and 10.4 m across.
• Were they precise?
• Were they accurate?
Significant Figures: Examples
Measured
Value
Uncertainty
Ruler
Division
Known
digits
Estimated
digit
1.07 cm
+/-0.01 cm
0.1 cm
1, 0
7
3.576 cm
+/-0.001 cm
0.01 cm
3,5,7
6
22.7 cm
+/- 0.1 cm
1 cm
2, 2
7
The Metric System: SI System
An easy way to measure
The Metric System
• Easier to use because it is a decimal
system
• Every conversion is by some power of 10.
• A metric unit has two parts
– A prefix and a base unit.
• prefix tells you how many times to divide
or multiply by 10.
SI Prefixes
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Exa
peta
tera
Giga
mega
kilo
Hecta
deca
Unit
Centi
milli
micro
Nano
pico
femto
Atto
Check blackboard for details
Fundamental Units
SI Unit
Name
Abbreviation
Length
Meter
M
Mass
Kilogram
Kg
Time
Second
s
Temperature
Kelvin
K
Electric
current
Ampere
A
Quantity of
matter
Mole
Mol
luminosity
Candela
Cd
Mass
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Quantity of matter
The same in the entire universe
Based on Pt/Ir alloy standard
1gram is defined as the mass of 1 cm3 of
water at 4 ºC.
• 1000 g = 1000 cm3 of water at 4 ºC
• 1 kg = 1 L of water 4 ºC
0ºC
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Measuring Temperature
Celsius scale.
water freezes at 0ºC
water boils at 100ºC
body temperature 37ºC
room temperature 20 - 25ºC
Measuring Temperature
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Kelvin starts at absolute zero (-273 º C)
degrees are the same size
C = K -273
K = C + 273
Kelvin is always bigger.
Kelvin can never be negative.
Absolute zero: temp. at which a system
cannot be farther cooled.