Download Scientific Notation

Objective
1. To write very large or very small numbers in
standard form, in scientific notation, and vice
versa.
• To compare and order numbers in scientific
notation
Designed by Skip Tyler, Varina High School
How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal
notation. When numbers get this large,
it is easier to write them in scientific
notation.
Scientific Notation
A number is expressed in scientific
notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Write the width of the universe in
scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make
this number be between 1 and 10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the
decimal?
23
When the original number is more than 1,
the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the
exponent is negative.
9.02 x 10-8
Why does a Negative Exponent give
us a small number?
10,000 = 10 x 10 x 10 x 10 = 104
1,000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 101
1 = 100
Do you see a pattern?
Sooooo
= 10-1
= 10-2
=
=
=
= 10-3
= 10-4
Write 28750.9 in scientific notation.
1.
2.
3.
4.
2.87509 x 10-5
2.87509 x 10-4
2.87509 x 104
2.87509 x 105
2) Express 1.8 x 10-4 in decimal
notation.
0.00018
3) 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
4) 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
5) 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
6) 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
7) 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 (2.8 x 103)(5.1 x 10-7) in
scientific notation.
1.
2.
3.
4.
14.28 x 10-4
1.428 x 10-3
14.28 x 1010
1.428 x 1011
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
8) 234.6 x
9
10
2.346 x 1011
9) 0.0642 x 104
on calculator: 642
6.42 x 10 2
Write 531.42 x 105 in scientific
notation.
1.
2.
3.
4.
5.
6.
7.
.53142 x 102
5.3142 x 103
53.142 x 104
531.42 x 105
53.142 x 106
5.3142 x 107
.53142 x 108
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
MULTIPLYING AND DIVIDING
Rule for Multiplication
When multiplying with scientific notation:
• Multiply the coefficients together.
• Add the exponents.
• The base will remain 10.
(2 x 103) • (3 x 105) =
6 x 108
(4.6x108) (5.8x106) =26.68x1014
Notice: What is wrong with this example?
Although the answer is correct, the number
is not in scientific notation.
To finish the problem, move the decimal one
space left and increase the exponent by
one.
26.68x1014 = 2.668x1015
((9.2
x 105) x (2.3 x 107) =
21.16 x 1012 =
2.116 x 1013
(3.2 x 10-5) x (1.5 x 10-3) =
4.8 • 10-8
Rule for Division
When dividing with scientific notation
1.Divide the coefficients
2.Subtract the exponents.
3.The base will remain 10.
(8 • 106) ÷ (2 • 103) =
4 x 103
Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) =
(3 x 105) x (7 x 104) =
(5.63 x 108) x (2 x 100) =
(4.55 x 10-14) x (3.77 x 1011) =
(8.2 x10-6) x (9.4 x 10-3) =
Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) = 2.62 x 10-1
(3 x 105) x (7 x 104) = 2.1 x 1010
(5.63 x 108) x (2 x 100) = 1.13 x 109
(4.55 x 10-14) x (3.77 x 1011) = 1.72 x 10-2
(8.2 x10-6) x (9.4 x 10-3) = 7.71 x 10-8
Please divide the following numbers.
1. (5.76 x 102) / (4.55 x 10-4) =
2. (3 x 105) / (7 x 104) =
3. (5.63 x 108) / (2) =
4. (8.2 x 10-6) / (9.4 x 10-3) =
5. (4.55 x 10-14) / (3.77 x 1011) =
Please divide the following numbers.
1. (5.76 x 102) / (4.55 x 10-4) = 1.27 x 106
2. (3 x 105) / (7 x 104) = 4.3 x 100 = 4.3
3. (5.63 x 108) / (2 x 100) = 2.82 x 108
4. (8.2 x 10-6) / (9.4 x 10-3) = 8.7 x 10-4
5. (4.55 x 10-14) / (3.77 x 1011) = 1.2 x 10-25
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
Raising Numbers in Scientific
Notation To A Power
(5 X 104)2 =
(5 X 104) X (5 X 104) =
(5 X 5) X (104 X 104) =
(25) X 108 = 2.5 X 109
Try These:
1. (3.45 X
1010)2
1.19 X 1021
• (4 X 10-5)2
1.6 X 10-9
• (9.81 X 1021)2
9.624 X 1043
1. (3.45 X 1010)2 = (3.45 X 3.45) X (1010 X 1010) = (11.9) X (1020)
= 1.19 X 1021
3. (4 X 10-5)2 = (4 X 4) X (10-5 X 10-5) = (16) X (10-10) = 1.6 X 109
•
(9.81 X 1021)2 = (9.81 X 9.81) X (1021 X 1021) = (96.24) X
(1042) =
9.624 X 1043
9.54x107 miles
1.86x107 miles
per second
Scientific
Notation
Makes
These
Numbers
Easy