Transcript Unit 2

Systems for Measurement
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SI (System International): Units are
an agreed upon set of scientific units
Based upon the metric system.
Metric system: Assigns basic units of
measurements and attaches prefixes to
change the units by factors of 10
In science we use the metric system
Basic measurements
Length or distance
Mass = the amount of matter in an object
Time
Temperature
Amount of substance = number of particles
Electrical current
Derived measurements
Volume derived from length
Velocity from distance and time
Density derived from mass and volume
Measurements are made by using
instruments
Instruments
Measurement
Instruments
Length
ruler, meter
stick, caliper
Mass
scale, balance
Time
watch
Temperature
thermometer
Volume
graduated
cylinder
Metric Units
Measurement
Basic Unit
Symbol
SI unit
Length
meter
m
m
Mass
gram
g
kg
Time
second
s
s
Volume
Liter
L
m3
Metric Prefixes
Prefix
Symbol
Multiplier
Giga
G
109 (1000000000)
Mega
M
106 (1000000)
Kilo
k
103 (1000)
BASE UNIT
(s, m, L, g)
Deci
d
10-1 (0.1)
Centi
c
10-2 (0.01)
Milli
m
10-3 (0.001)
Micro
m
10-6 (0.000001)
Nano
n
10-9 (0.000000001)
Sig-Figs
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No measurement is exact; each instrument
has its own uncertainty associated with it.
Significant Figures (Significant Digits):
All digits in a measurement through the first
uncertain digit.
Sig-Figs
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Our balances give a measurement of 4.36g.
Remember, the uncertainty is 0.01g.
This means that the value is between 4.35g
and 4.37g.
Thus all of the digits are significant…that is,
they tell us something useful.
Sig-Figs
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We would not report this value as
4.36000000g because we know the
value is between 4.35g and 4.37g.
(The zero’s after the 6 are insignificant,
they don’t tell us anything useful.)
Determining the Number of
Sig-Figs
1. All non-zero digits are significant
Example:
4 significant digits
1999 L
2. Zeros between non-zero digits are significant
Example:
9.006 cm 4 sigs
100.1 s
4 sigs
3. Zeros that come before non-zero integers are
not significant
These are called placeholder zeros
Example:
0.000036
0.00106
2 sigs
3 sigs
4. The zeros that come after non-zero
integers and after the decimal point
are significant
Example:
0.930 3 sigs
0.0005060 4 sigs
Determining the Number of
Sig-Figs
5. Zeros to the right of large numbers with no
decimal point are not significant
Example:
100 1 sigs
1238600 5 sigs
100.
3 sigs
Sig-Fig Problems
a)10830
b) 0.00260
c) 1001.0
d) 0.00006
Scientific Notation
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Scientific notation: number is written as
a quantity between 1 and 10 multiplied by
10 raised to a power
Scientific Notation
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Positive exponents mean the decimal place is
moved to the right that many times
If there is open spots fill them with zeros
Example:
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1.032 x 104
=1.032 0 =10320
Scientific Notation
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Negative exponents mean the decimal
place is moved to the left
Example:
2.86 x 10-3
= 0 0 2.86 =.00286
Scientific Notation
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The reverse holds true when forming
numbers in scientific notation
If the decimal point is moved to the left the
power on 10 is positive
Example:
29836 = 2.9836 x104
Scientific Notation
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If the decimal point is moved to the
right the power on 10 is negative.
Example:
-4
=
3.68
x
10
0.000368
Scientific Notation Problems
Convert the following from scientific notation:
a) 6.82 x 105
b) 3.10 x 10-3
c) 2.06 x 101
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Convert the following to scientific notation:
a) 12345
b) 0.000612
c) 10300000
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Scientific Notation
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Entering numbers in scientific notation
in the calculator using the EE or exp
button.
When doing this DO NOT enter the
number x 10 then the EE or exp power.
Calculations Involving Sig-Figs
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In multiplication and division, the result
will have the same number of sig-figs as
the quantity with the fewest number of
sig-figs.
Example: 6.834  2.0 = 3.417  3.4
1.010 * 1.0 = 1.0
4 sig-figs
22sig-figs
sig-figs
2 sig-figs
4 sig-figs
2 sig-figs
Calculations Involving Sig-Figs
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In addition and subtraction, the result
will have the same number of sig-figs
after the decimal point as the quantity
with the fewest sig-figs after the
decimal point.
The limiting factor is the quantity with
the greatest uncertainty.
Calculations Involving Sig-Figs
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Example
296 3 sig-fig
10368.256 3 sig-figs after the .
1892 4 sig-fig
- 10368.21 2 sig-figs after the .
+ 10100 3 sig-fig
0.046
12288  12300
2 sig-figs
3 sig-fig
after the
.
Rules For Rounding
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Decimal notation is the "usual"
way numbers are written
Sometimes it is necessary to round
numbers to the correct of significant
digits, especially after calculations.
Rules For Rounding
1. If the 1st number to be dropped is less than 5, leave
the preceding number unchanged.
2. If the 1st number to be dropped is greater than 5 or
5 followed by non-zeros, increase the
preceding number by 1.
3. If the number to be dropped is exactly 5 followed by
zeros
- increase the preceding number if it is odd
- leave the preceding number unchanged if
it is even
Precision and Accuracy
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Precision: How close individual
measurements are
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Reproducibility
Checked by repeating measurements
Poor precision id from poor lab techniques
Precision and Accuracy
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Accuracy: How close a result is to the
“true” value
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Correctness
Checked by using another method
Poor accuracy is from procedural or
equipment flaws
Precision and Accuracy
Good Precision,
Bad Accuracy
Good Accuracy, Bad
precision
Precision and Accuracy
Good Accuracy,
Good Precision
Bad Accuracy,
Bad Precision