Scientific Notation
Rational and Irrational Numbers
Scientific Notation
4.632 x
Coefficient
is 4.632
6
10
Base
is 10
Exponent
is 6
Scientific Notation Rules
4.632 x 106
The coefficient is always larger than
or equal to 1, and smaller than 10.
The base is always 10.
The exponent is positive for large
numbers, and negative for numbers
between 0 and 1.
Why use Scientific Notation?
• The speed of light is 300,000,000 m/sec
• The speed of light is often represented by the
letter c.
• It is a large number used in many calculations
(E = mc2)
• In scientific notation it is written 3.0 x 108
• It is easier to calculate with large numbers in
scientific notation.
How does Scientific
Notation Work?
• 14 0,000,000,000
• 1.4
x
standard form
What number
goes here?
?
10
• 1.4 x 1011
scientific notation
Scientific Notation: Great
for very small numbers
• The size of a dust particle is about
0.000 000 000 752 kilograms
• 0.000 000 000 752
• 7.52
standard form
x 10? what number goes here?
• 7.52 x 10-10
scientific notation
What does Scientific
Notation look like on the
HP 39G ?
Find the EEX key
To access these
second functions,
you need to hit the
SHIFT key
Using the HP 39 G
• Enter the following number:
• 3.4 x 1011
• 3.4
shift
EEX 11 enter
• Standard form: 340,000,000,000
• Notice that both the scientific form
and the standard form are
displayed on the screen
Using the HP 39 G
• Enter the following number:
• 2.46 x 10-9
• 2.46
SHIFT EEX
(-)
9
The sun is about (1.5 x 1011) meters
from the earth. Light travels at
approximately (3.0 x 108) meter/sec.
How many seconds does it take for
light to travel from the sun to the
earth? (distance = speed x time)
a) 50 seconds
b) 5.0 x 102 seconds
c) 5.0 x 103 seconds
Thiomargarita namibiensis is the
largest known species of bacteria
and is approximately 7.5 x 10-4 m
wide. The average bacterium is
about the size of Escherichia coli
and is about 1.5 x 10-6 m wide.
What is the difference in widths of
the two species?
a) 74.9 x 103 m
b) 7.5 x 10-1 m
c) 7.5 x 10-4 m
E. coli
T. namibiensis
Solve and express the
answer in scientific notation:
( 2.45 x 105 ) x (5 x 103 )
a)
b)
c)
d)
1.225 x 109
12.25 x 108
1.225 x 1015
12.25 x 1015
Classifying Numbers
• Numbers can be classified
• For instance, we can pick out all of the
numbers that are divisible by 2. They are
classified as even numbers.
• We can also classify numbers in other
ways.
Rational and Irrational
• Numbers can be classified as
rational numbers.
• Rational numbers are numbers that
can be written as fractions.
• In decimal form, rational numbers
are either
terminating or repeating.
Terminating numbers
• A terminating number is a number
that terminates, which means ends.
• Examples of terminating numbers:
3.14
4.5678932221
0.33339
• Examples of numbers that do
NOT terminate
3.333333… pi
0.121231234….
Repeating Numbers
• A repeating number is a number that
does not terminate, but it repeats over
and over EXACTLY THE SAME
• Examples of repeating numbers:
3.33333…. 4.34343434……
Examples of NON-repeating numbers:
3.343453456…..
pi
9.352109….
Rational vs. Irrational
• If a number in decimal form repeats
exactly, or terminates, then it is a
rational number.
• If a real number is NOT rational,
then it is irrational.
Real Numbers
• Another classification of numbers is the
set of numbers called Real Numbers.
• This one is easy. Real numbers are the
rational numbers and the irrational
numbers combined.
• Real = Rational + Irrational
• Place the following numbers in order
from least to greatest.
-7, 14/3, 280%, 1 3/7
Step 1. Change into decimals.
Step 2. Place on a number line.
-7 = -7
14/3 = 14 divided by 3  4.7
280% = 280 divided by 100  2.8
1 3/7 = 1 + 3/7  1.43
-7
1 3/7
280% 14/3
0
Order from least to greatest: -7, 1 3/7, 280%, 14/3