Download 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)
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 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
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 Zeroes
3 Rules for determining if a zero is
significant:
1. Leading zeroes never count

0.001, .01
2. Trapped zeroes always count

101, 2087, 400,513
3. Trailing zeroes only count if there is
a decimal point anywhere in the
number

100.0, 300., 0.02300, .9850000
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 to
the nearest 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




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