Transcript PP 6b Scientific Notation

SCIENTIFIC NOTATION
A QUICK WAY TO WRITE
REALLY, REALLY
BIG
OR
REALLY, REALLY SMALL
NUMBERS.
Mathematicians
are Lazy!!!
They decided that by
using powers of 10, they
can create short versions
of long numbers.
Scientific Notation
A number is expressed in scientific
notation when it is in the form
a x 10n
where a is from 1 to 9
and n is an integer
23 X 105 is not in proper
scientific notation. Why?
Soooo
137,000,000 can be rewritten
as
1.37 X
8
10
Now You Try
Using scientific notation,
rewrite the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104
Try These
4,000
4 X 103
2.48 X 103
2,480
6.123 X 106
6,123,000
306,000,000
3.06 X 108
Your Turn
Using Scientific Notation,
rewrite the following numbers.
0.000882
8.82 X 10-4
0.00000059
5.9 X 10-7
0.00004
4 X 10-5
More Examples
1) 0.0004
2)
3)
4)
5)
4 X 10-4
1.248 X 10-6
.000001248
6.123 X 10-5
.00006123
0.00000306
3.06 X 10-6
0.000892
8.92 X 10-4
Using your calculator
Express 4.58 x 106 in decimal notation.
4,580,000
On the graphing calculator, scientific
notation is done with the
button.
4.58 x 106 is typed 4.58
6
Use a calculator to evaluate:
4.5 x 10-5
1.6 x 10-2
Type 4.5
-5
1.6
-2
You must include parentheses if you don’t use
those buttons!!
(4.5 x 10
-5)
(1.6 x 10
-2)
0.0028125
Write in scientific notation.
2.8125 x 10-3
Use a calculator to evaluate:
7.2 x 10-9
1.2 x 102
On the calculator, the answer is:
6.E -11
The answer in scientific notation is
6 x 10 -11
The answer in decimal notation is
0.00000000006
Use a calculator to evaluate
(0.0042)(330,000).
On the calculator, the answer is
1386
The answer in decimal notation is
1386.
The answer in scientific notation is
1.386 x 103
Use a calculator to evaluate
(3,600,000,000)(23).
On the calculator, the answer is:
8.28 E +10
The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
234.6 x
9
10
2.346 x 1011
0.0642 x 104
on calculator: 642
6.42 x 10 2