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MEASUREMENT
Scientific Notation
Science often involves working with very large or
very small numbers.
Ex. Speed of light = 300,000,000 m/s
Speed of snail = 0.00086 m/s
Scientific notation makes very large or very
small numbers easier to work with.
Scientific Notation
Scientific notation = a way of expressing a value
as the product of a number
number between
between 11 and
and 10
10
and a power of 10
10.
300,000,000 m/s
3.0 x 108
The exponent (8) tells you that the decimal is 8
places to the RIGHT.
Scientific Notation
For numbers less than 1, the exponent is
NEGATIVE.
0.00086 m/s
8.6 x 10-4
The negative exponent tells you how many
decimal places there are to the LEFT of 8.6.
Practice
Write 9.8 x 108 in standard notation.
9 8 0 0 0 0 0 0 0
Write 7.5 x 10-8 in standard notation.
0 0 0 0 0 0 0 0 7 5
Practice
Write 6,500,000 in scientific notation.
6.5 x 106
Write 0.0000056 in scientific notation.
5.6 x 10-6
Multiplying
Multiplying numbers in scientific notation
– Multiply the numbers that appear before the
multiplication signs
– Add the exponents
(3.0 x 108) x (5.0 x 102) = 15 x 1010 = 1.5 x 1011
Dividing
Dividing numbers in scientific notation
– Divide the numbers that appear before the
multiplication signs
– Subtract the exponents
1.5 x 1011 = 0.50 x 103 = 5.0 x 102
3.0 x 108
SI Units
SI Units = International System of Units
Using SI as the standard system of measurement
allows scientists to compare data and
communicate with each other about their
results.
SI Base Units
QUANTITY
UNIT
SYMBOL
Length
Meter
m
Mass
Kilogram
kg
Temperature
kelvin
K
Time
Second
s
SI Derived Units
Quantity
• Area
Kilogram
Unit
Symbol
Square meter
m2
Volume
• kg
Cubic meter
m3
Kg/m3
Pressure
Kilograms per
cubic meter
• K 2)
pascal (kg/m∙s
joule (kg∙m2/s2)
J
• Density
Temperature
• kelvin
• Energy
Time
• Frequency
Second
hertz (1/s)
• s
Pa
Hz
Metric Prefixes
lsua.info
Limits of Measurement
Precision = how exact a measurement is
Which of the clocks is more precise?
Significant Figures
Significant Figures = all the digits that are
known in a measurement, plus the last digit that
is estimated.
The fewer the significant figures, the less precise
the measurement.
How long does it take you to eat breakfast?
5 minutes
1 sig fig
5 minutes, 15 seconds
5.25 minutes
3 sig figs
The digital
clock is more
PRECISE
Accuracy
Accuracy = the closeness of a measurement to
the actual value of what is being measured.
If clock is 15 minutes slow, it
may be precise but it is
NOT ACCURATE.
Temperature
Common Temperatures
Fahrenheit (°F)
Celsius (°C)
kelvin (K)
Water boils
212
100
373
Human body
98.6
37
310
Average room
68
20
293
Water freezes
32
0
273
0 kelvin refers to the lowest possible
temperature that can be reached. This would be
-273 °C, -459°F.
Significant Figures Rules
1. All NONZERO digits are significant
1.234 g = 4 sig figs
1.2 g = 2 sig figs
2. Zeros between nonzero digits are significant
1002 kg = 4 sig figs
3.07 mL = 3 sig figs
Significant Figures Rules
3. Zeros to the LEFT of the first nonzero digit are
NOT significant- placeholder
0.001 g = 1 sig fig
0.012 = 2 sig figs
4. Trailing zeros to the right of the decimal in a
number are significant
0.560 mL = 3 sig figs
0.20 g = 2 sig figs
Significant Figures Rules
5. Zeros at the end of a number (not to the
right of a decimal) are not necessarily
significant
190 miles = 2 or 3 sig figs
50,600 cal = 3,4, or 5 sig figs
When in doubt, convert the number to scientific
notation.
506,000 = 5.06 x 105 = 3 sig figs
Quiz!
Take out a half sheet of paper. (Tear one in half
and share with your neighbor)
Put your name on the paper.
Label 1-5
Question #1
Why do scientists use scientific notation?
Question #2
Convert the following number to scientific
notation:
0.000 000 000 079
Question #3
Solve this problem.
(8.0 x 105)/(4.0 x 103) =
Question #4
What is the SI Unit for mass?
Question #5
Is this an example of precision or accuracy?