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Objective1. 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?
23When 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?
9.02The decimal was moved how many places?
8When 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. 2.87509 x 10-5
2. 2.87509 x 10-4
3. 2.87509 x 104
4. 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)
0.0028125Write 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 is1386.
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. 14.28 x 10-4
2. 1.428 x 10-3
3. 14.28 x 1010
4. 1.428 x 1011
Write in PROPER scientific notation.(Notice the number is not between 1 and 10)
8) 234.6 x 109
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. .53142 x 102
2. 5.3142 x 103
3. 53.142 x 104
4. 531.42 x 105
5. 53.142 x 106
6. 5.3142 x 107
7. .53142 x 108
PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC
NOTATIONNOTATION
MULTIPLYING AND DIVIDINGMULTIPLYING 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) =
(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) =
2.62 x 10-1
2.1 x 1010
1.13 x 109
7.71 x 10-8
1.72 x 10-2
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
Please divide the following numbers.
PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC
NOTATIONNOTATION
Raising Numbers in Scientific Raising Numbers in Scientific Notation To A PowerNotation 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
1. (3.45 X 1010)2
2. (4 X 10-5)2
3. (9.81 X 1021)2
Try These:
1. (3.45 X 1010)2 = (3.45 X 3.45) X (1010 X 1010) = (11.9) X (1020) = 1.19 X 1021
2. (4 X 10-5)2 = (4 X 4) X (10-5 X 10-5) = (16) X (10-10) = 1.6 X 10-9
3. (9.81 X 1021)2 = (9.81 X 9.81) X (1021 X 1021) = (96.24) X (1042) = 9.624 X 1043
1.19 X 1021
1.6 X 10-9
9.624 X 1043
9.54x107 miles
1.86x107 milesper second
Scientific Notation Makes These Numbers Easy