Scientific
Measurements
BIG NUMBERS
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Scientists often work with very large numbers.
National debt = $5,653,000,000,000
Bill Gates' net worth = $57,030,000,000
Distance to Alpha Centauri =
40,120,000,000,000,000 m
Distance to Andromeda Galaxy =
21,800,000,000,000,000,000,000 g
Mass of Sun =
1,990,000,000,000,000,000,000,000,000,000,00
0g
Small numbers
Scientists often work with very small
numbers.
 Radius of hydrogen atom =
0.000000000052918 m
 Mass of Hydrogen atom =
0.0000000000000000000000016733 g
 Mass of electron =
0.00000000000000000000000000091096
g
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What to do?
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Scientific notation – way of expressing
a value as the product of a number
between 1 and 10 and a power of 10.
Examples
300,000,000
 Move the decimal 8 places to the left
 = 3 x 108
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750,000
 Move the decimal 5 places to the left
 = 7.5 x 105
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More Practice
230,000,000
 2.3 x 108
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40,000
 4 x 104
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34,000,000
 3.4 x 107
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Scientific Notation cont.
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Scientific notation can also be used to
write out very small numbers.
0.0005
 Move the decimal 4 places to the right
 5 x 10-4
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More Practice
0.000002
 = 2 x 10-6
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0.0045
 = 4.5 x 10-3
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0.000075
 = 7.5 x 10-5
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Practice - Reverse
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3 x 103
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= 3,000
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4 x 106
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= 4,000,000
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3.4 x 105
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= 340,000
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2.0 x 104
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= 20,000
More Practice
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6 x 10-5
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= 0.00006
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4.5 x 10-2
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= 0.045
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3.5 x 10-3
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= 0.0035
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5.5 x 10-7
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= 0.00000055
Reliability in Measurements
 Precise
measurements
will give the
same results
again and again
 Accuracy is how
close you are to
the accepted
value
Where would you measure?
Certainty in Measurement
Significant digits are those digits
that are certain in your measurement
plus one estimated
 In order to count significant digits just

count the digits
5.6
 781
 6,778
 What about large or small numbers?
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BIG NUMBERS
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Scientists often work with very large numbers.
National debt = $5,653,000,000,000
Bill Gates' net worth = $57,030,000,000
Distance to Alpha Centauri =
40,120,000,000,000,000 m
Distance to Andromeda Galaxy =
21,800,000,000,000,000,000,000 g
Mass of Sun =
1,990,000,000,000,000,000,000,000,000,000,00
0g
Small numbers
Scientists often work with very small
numbers.
 Radius of hydrogen atom =
0.000000000052918 m
 Mass of Hydrogen atom =
0.0000000000000000000000016733 g
 Mass of electron =
0.00000000000000000000000000091096
g

Atlantic Pacific Rule
 If
decimal is Absent
starting from the
right count all digits
after the 1st non
zero
 If decimal is
Present starting
from the left count
all digits after the
1st non zero
Practice
 4500
Liters
 0.00543 grams
 0.00607000 seconds
 500,003 meters
 400,000. Joules
 5000340035.000 Amps
Exact Numbers
 Remember
that the rules of Sig Figs
only apply to measurements and not
exact numbers.
 Years in a century
 Students in a classroom
 Centimeters in a meter
Rounding Sig Figs
 Remember
to keep the value of
the number the same.
 Remember
5 or more.
– Round
– Round
– Round
– Round
– Round
to round up if last digit is
12.5 to 2 sig figs
56.99392882 kg to 3 sig figs
.00027262299 mL to 4 sig figs
303 meters to 3 sig figs
303 meters to 2 sig figs
Multiplying / Dividing SigFigs
 When
multiplying/dividing
measurements you are limited by the
measurement with the least number of
significant digits.
Practice
 Area
=LxW
 Length = 6.15 m
 Width = 4.026 m
 Volume = L x W x H
 Volume = 3.05 x 2.10 x 0.75
SI Units
 SI
units: a revised form
of the metric system
 SI base units are
fundamental units all
other units are based
upon
Base Units
Physical Quantity
Name of SI unit
Symbol for SI unit

length
meter
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
temperature
Kelvin
K
amount of substance
mole
mol
luminous intensity
candela
cd
Derived units

Derived units are made from a
combination of base units.
Examples:
 Volume
 Density
Examples of SI derived units expressed in terms of base units
Derived quantity
SI derived unit
Name
Symbol
area
square metre
m2
volume
cubic metre
m3
speed, velocity
metre per second
m/s
acceleration
metre per second squared
m/s2
wavenumber
1 per metre
m-1
density, mass density
kilogram per cubic metre
kg/m3
specific volume
cubic metre per kilogram
m3/kg
current density
ampere per square metre
A/m2
magnetic field strength
ampere per metre
A/m
Converting Metric Units
 SI
units based upon factors of 10
 Begin with the prefix given and move
the decimal the same number and
direction to the desired prefix
 Know the prefixes and values: The
ones most important for us are Kilo
(1,000), Centi (.01) and Milli (.001)
Others can be looked up as needed or
will be given in the problem.
Practice
A
soda can holds 355 mL convert to
L
 Convert 76 km to meters
 Convert 18 mm to cm
 A Thumb drive holds 512 Megabytes
convert to Kilobytes
 Violet Light has a wavelength of 430
nm convert to km
Ratios
 Ratios
are a common way of
expressing results in Chemistry
 Teacher to student ratio
 Velocity
 Population Density
 Density
 Ratios of chemicals in a chemical
reaction
Finding Density
Density = Mass / Volume
 Units are (kg/m3) or (g/mL)

Lets calculate Density
 Mass = 27 kg
 Volume = 3.0 mL
 Denstiy = 9.0 kg/mL
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More Practice
Mass = 45 kg
 Volume = ???? mL
 Density = 5.0 kg/mL
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Practice
Mass = 10.0 g
 Volume of water only = 35.0 mL
 Volume of water w/ Object = 40.0 mL
 Volume of object only = __________
 Density = ______________
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Practice
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An aquarium has dimensions of 25.0 cm
by 68.5 cm by 34.0 cm. If the mass of
the aquarium if 2.3 kg, calculate the
density.
The density of air is 0.0013 g/cm3 . How
much mass does air have in a volume of
400. cm3?
Water & Density
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Water has a density of
1.0 g/ml at 4o C
Water’s mass in grams
is equal to its volume
in mL
Any object with a
density greater will
sink. . . less will float
1cm3 = 1cc = 1ml
Percent error
There is always some error in your measurement.
It is unavoidable.
To calculate use the following formula:
% Error = ((measured value – accepted value)/
accepted value ) X 100 %
or % error = ((O - A)/A ) X 100 %
PERCENT ERROR CAN BE NEGATIVE !!!
In Science, a negative percent error means your
value was less than the accepted value. This is very
common in Chemistry.
Practice
•
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When measuring the density of gold you
find a value of 20.9 g/cm3 . The
accepted value is 19.3 g/cm3. What is
your error ?
Samantha S. Sloppiness measured the
volume of her soda before she drank it
for her midmorning snack. She measured
the volume of the 12 oz. bottle to be 10
oz. What is her error ?
Answers
((20.9 – 19.3) / 19.3 ) x 100 %
= 8.29 %
Notice it is a positive number since the
answer was more than the real value.
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#1
((10 – 12) / 12 ) x 100 %
= - 16.67 %
Notice it is a negative number since the
answer was less than the real value.
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#2