Transcript Standard Units, Sig Figs, and Scientific Notation

Standard Units, Sig Figs, and
Scientific Notation
What are Standard Units?
Numbers by themselves are not exact
enough to describe properties of matter
SI system: standard scientific system
of measurement (also called metric
system)
Combinations of base units can be used
to describe nearly all physical
measurements
What are the Base Units?
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)
How Can Scale Be Expressed
Using Base Units?
Prefixes used with base units establish
appropriate scale
Prefixes can modify the SI unit to match
the scale
What are the Most Commonly
Used Prefixes?
Milli0.001
Centi0.01
Deci0.1
Base
1
Deca10
Hecto- 100
Kilo- 1000
(m)
(c)
(d)
(D)
(H)
(k)
How is Temperature Different?
Measurements in the lab are made on
the Celsius scale, then converted to K
Conversion: K = °C + 273
Kelvin scale does not use the degree
symbol when reporting the temp
Kelvin temperatures are always positive
Based on absolute zero (-273.15 °C)
What are Derived Units?
Derived units: created by multiplying
or dividing the seven base units in
various ways
Examples: m/s, cm3
How Reliable Are Measurements?
No measurement obtained in the lab is exact;
ALL measurements have some error
Sources:



Instrumental error: instrument not calibrated
correctly
Human error: occur by chance or through bias
Method error: incorrect procedure or poor design
of experiment
What is the Difference Between
Accuracy and Precision?
Accuracy: how close a measurement
comes to the true accepted value
Precision: degree of exactness or
refinement of a measurement
Because measurements differ in
precision, when calculation are
performed, significant digits MUST be
taken into consideration
What are Significant Figures?
There are rules to determine when
figures are significant:


All nonzero digits are significant.
Examples:
 138475
 456.32
 129
Rules for Significant Figures
Zeroes are significant if:

They are between nonzero digits
 Examples:



803
1.05
5007
Rules for Significant Figures
Zeroes are significant if:

They are to the RIGHT of a decimal point
AND also to the right of a significant digit
 Examples:




18.30
703.0
13.5600
240.00
Rules for Significant Figures
Zeroes are significant if:

A line is drawn over it
 Examples:
Rules for Significant Figures
Zeroes are significant if:

A decimal point is expressed
 Example:


800.
1000.
Rules for Significant Figures
A zero is NOT significant if:

It is used to show how big or how small a
number is (i.e., it is used as a place holder)
 Examples:

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
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
1800
34,200
100
0.75 (leading zeroes)
0.00345
Rules for Significant Figures
A zero is NOT significant if:

It is a single zero before a decimal point
with no nonzero number to the left of it
 Examples:


0.5528
0.011
What is Uncertainty?
The degree of estimation used in a
measurement
Measurements are uncertain for two
reasons:


Instruments are never completely flawless
Measuring always involves some estimation
What is Uncertainty?
When measuring, write down all the certain
digits that the instrument can give you plus
one uncertain digit that you can estimate
On a digital display, the last digit is the
estimated digit
On a scale, or graduations on equipment, the
last digit must be estimated by the measurer
How Can the Uncertain Digit
Be Determined?
To determine the uncertain digit:

Find the smallest increment on the scale of
the instrument
 increment: distance between markings on
equipment


Divide the distance by two
The last digit recorded will be a multiple of
half of the smallest increment
How Are Numbers Rounded?
Look at the digit next to the one to be
rounded.
Round up if the digit is >5

2.536  2.54 (rounded to 3 sig figs)
Round down if the digit is <5

2.534  2.53
How is the Digit “5” Rounded?
If the 5 is followed by a number that is
a nonzero number, round up

2.5351 2.54
If the 5 is followed by a zero, round up
the 5 if it is next to an odd number;
round down if it is next to an even
number

2.5350  2.54; 2.5250  2.52
What are the Rules for Basic
Operations Using Sig Figs?
Addition and Subtraction:

Round answer to the least number of
decimal places in any of the numbers that
make up the answer
 Example: 18.31112 + 32.728
 Example: 86.432 - 10.
What Are the Basic Rules for
Multiplication and Division?
Round to the least number of significant
figures in any of the factors
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
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Example:
Example:
Example:
Example:
48.2 x 1.6 x 2.12
16.4/4.1
3 x 42.59 x 16.5
15.535/2
What is Scientific Notation?
A number expressed as the product of two
factors
The first number is between 1 and 10
Uses only the sig figs of the original number
The second number is a power of ten
Exponent found by counting the number of
times the decimal point must be moved to
make the first number between 1 and 10
What is Scientific Notation?
Example:
120000 = 1.2 x 105
1405000
750670000
What is Dimensional Analysis?
A method of converting from one
measurement to another using
conversion factors

conversion factor: fraction of equivalent
values to express the quantity in different
ratios
 Always equal to one
How is Dimensional Analysis Used?
Examples:
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Convert 15 mm to m
Convert 50 L to mL
Convert 32 in to m
What is Percent Error?
Method of evaluating the accuracy of a
measurement
Ratio of error to an accepted value
Formula:
% Error= Measured Value - Accepted Value x 100
Accepted Value