MEASUREMENT
OF MATTER
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■
Matter can be measured or described:
1.
Qualitatively - a descriptive which reflects the quality of
something in size, appearance, value, etc
2.
Quantitatively - relating to, measuring, or measured by
the quantity of something
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Units and Dimensions
■ In order to make quantitative observations,
measurements are needed.
■ When we measure properties of matter, we must
compare it with a known standard.
■ Measurements are therefore expressed with a
value and unit.
■ The scientific system of measurement is referred
to as the Système Internationale (SI) or the
International System of units.
– Based on the metric system,
– Seven fundamental quantities.
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Fundamental (Base) SI
Quantities
Quantity
Unit
Symbol
Mass
Kilogram
kg
Length
Metre
m
Time
Second
s
Temperature
Kelvin
K
Electric current
Ampere
A
Amount of substance
Mole
mol
Luminous intensity
Candela
cd
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5
Derived Quantities
■
These are some commonly used units which are
combinations of the fundamental (base) quantities.
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Prefixes in the SI
■
SI units are modified through the use of prefixes when they
refer to either smaller or larger quantities.
Prefix
Symbol Multiple of
Base
Prefix
Symbol
Multiple
of Base
tera
T
1012
deci
d
10-1
giga
G
109
centi
c
10-2
mega
M
106
milli
m
10-3
kilo
k
103
micro
µ
10-6
hecto
h
102
nano
n
10-9
deka
d
10
pico
p
10-12
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Scientific Notation
■
Used when writing very large or small numbers in a
convenient standard form.
■
Express the following quantities in scientific notation:
– (a) The diameter of a sodium atom, 0.000 000 000
372 m
– (b) The distance from the Earth to the Sun,
150,000,000,000 m
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Conversions
■
Converting between units is necessary at times.
– ___ K = 20°C
– 1 kg = ___ g
– 10 µg = __ g
– 10 µg = __ kg
– 1 m3 = __ cm3
– 280 m/s = ___ km/hr
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Significant Figures
■
The number of significant figures for a measurement is
the total number of digits recorded.
■
For example:
– mass of ball = 54.07 g
– 4 significant figures
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Rules for Determining # of
Significant Figures
■
All non-zero digits are significant.
■
Zeros in the middle of a number are always significant.
■
Exact numbers can be considered to have an unlimited
number of significant figures.
■
Zeros at the beginning of a number are not significant;
they act only to locate the decimal point.
– 0.006 61 g has three significant figures.
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Rules for Determining # of
Significant Figures
■
Zeros at the end of a number and after the decimal point
are always significant.
– These zeros would not be shown unless they were
significant.
– 55.220 K has five significant figures
■
Zeros at the end of a number and before the decimal
point may or may not be significant. E.g. 7500 m
– If number is expressed in scientific notation, then
every # is significant.
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Significant Figures in
Numerical Calculations
■
When adding or subtracting, the final answer cannot
have more decimal places than any of the original
numbers.
– 15.02 g + 9986.0 g + 3.518 g
= 10,004.538 g
■
When multiplying or dividing, the final answer cannot
have more significant figures than any of the original
numbers.
– 14.79 cm x 12.11 cm x 5.05 cm
(4 s.f.)
(4 s.f.)
(3 s.f.)
3
=904 cm
(3 s.f.)
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Precision and Accuracy
• Accuracy refers to how close a given measurement is to the
true value.
• Precision refers to how well a number of independent
measurements agree with one another.
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Accuracy of
Measurements
■
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Accuracy of
Measurements
■
When adding or subtracting measurements, their
absolute uncertainties are added.
■
When multiplying or dividing, their relative uncertainties
are added.
■
If objects are too small for adequate reading by the
instrument, then a large number of the objects can be
measured and the reading can be divided by the number
of objects. (The AU is also divided by the number of
objects.)
– E.g. 100 lead beads displaces 14.5 ± 0.5 cm3 of
water in a measuring cylinder.
– Avg vol of one lead bead = 14.5 /100 ± 0.5/100 cm3
= 0.145 ± 0.005 cm3
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