Transcript Scientific Notation

Chapter 1
Section 3
Measurement
Scientific Notation
Makes very large or very small numbers easier to
work with
(examples: 2,630,000,000,000,000,000 is much
easier to read and do calculations when written
as 2.63 x 1018, and 0.000000000000059 is easier
to use when written as 5.9 x 10-14.)
A way of expressing a number as a product of a
number (between 1 and 10) and a power of 10
The exponent on the 10 tells you how many places
the decimal has been moved
A positive power of 10 is a number larger than 1, so
multiplying by a positive power of 10 must give a
larger number
Example: 3.46x 105 = 346000; which is the 3.46 with
the decimal place moved 5 places to the right (to
make it a big number).
A negative power of 10 is a number smaller than
one, so multiplying by a negative power of 10
must give a smaller number
Example: 2.67 x 10-6 = 0.00000267; which is the
2.67 with the decimal place moved 6 places to
the left (to make it a small number)
In short :
positive power of 10 = big number = move right
negative power of 10 = small number = move left
positive power of 10 = big number = move right
103 = 10•10•10 = 1000
negative power of 10 = small number = move
left
10-3 = 1/10 • 1/10 • 1/10 = 1/1000
SI Units of Measurement
(Système International d’Unités)
International System of Units
A revised version of the metric system used by
scientists
The seven base units are metric units
The derived are combinations of the base units
Metric prefixes indicate what power of 10 something
should be multiplied/divided by
Derived Units
Quantity
Unit
Symbol
Area
Square meter
M2
Volume
Cubic meter
M3
Density
Kilograms per cubic meter
kg/m3
Pressure
Pascal (kg/m•s2)
Pa
Energy
Joule (kg•m2/s2)
J
Frequency
Hertz (1/s)
Hz
Electric charge
Coulomb (a•s)
C
Limits of Measurement
Precision is how exact a measurement is
Significant Figures (digits) are all of the digits that are
known in a measurement plus the last digit that is
estimated
The precision of a calculated answer is limited by the
least precise measurement used in the calculation
Example: You weigh a block of iron to be 25.68 g, and
measure the volume to be 3.3 cubic cm. You calculate
the density as 25.68 g / 3.3 cm3 = 7.781818182 g/cm3.
Your least precise measurement had only 2 significant
figures, so your answer can have only 2 significant
figures 7.8 g/cm3
Accuracy
Accuracy is the closeness of a measurement to
the actual value of what is being measured.
Precise – repeatable and reliable;
getting the same measurement each time
Accurate – capable of providing a correct
reading or measurement;
getting the correct reading or measurement