Section 8.3: Scientific Notation
Objective
The student will be able to:
• Express numbers in scientific and decimal
notation
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.
Who uses this?
• Astronomers often work with very large
numbers such as the masses of planets. The
mass of each planet in the solar system is
given on the next slide. Notice each value is
written as the product of a number and a
power of 10. These values are written in
scientific notation.
Scientific Notation in Astronomy
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
3.30x10^23
4.87x10^24
5.97x10^24
6.42X10^23
1.90x10^27
5.69x10^26
8.68x10^25
1.02x10^26
1.27x10^22
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
Positive Exponents (large #’s)
Example 1:
2.45 x 108
Example 2:
2.19 x 105
Example 3:
30,500,000
Example 4:
3,022,000,000,000
Ex. 5) 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
Negative Exponents (small #’s)
• Example 6:
3 x 10-5
• Example 7:
7.48 x 10-3
• Example 8:
0.000000672
• Example 9:
0.000781
10) You Try: Write 28750.9 in scientific
notation.
A. 2.87509 x 10-5
B. 2.87509 x 10-4
C. 2.87509 x 104
D. 2.87509 x 105
You Try a few…
A) 2 x 10-8
B) 4.59 x 103
C) 7.183 x 1014
D) 3.6 x 10-5
E) 56,700,000
F) 0.00567
G) 0.00000000004
Review
Positive Exponents = LARGE numbers
• Move the decimals to the RIGHT
Negative Exponents = SMALL numbers
• Move the decimals to the LEFT
11) Express 1.8 x 10-4 in decimal notation.
0.00018
12) 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
You Try:
• Find YOUR textbook and complete the
following: page 402 #16-44 Odd, 46-53
• Turn in for a CW grade. Please ask the
neighbor for assistance.
Warm-Up, Write the following in scientific
notation
1. 984000000
2. 0.00058
3
3. 560 x 10
Answer Key
• 1. 9.84 x 108
• 2. 5.8 x 10-4
5
• 3. 5.6 x 10
There is more to sci. notation
• Numbers in scientific notation can be
multiplied or divided. First multiply the
decimals, then apply the product of powers or
quotient of powers property to simplify the
powers of 10. Next, rewrite the decimal in
scientific notation and simplify the powers..
Let’ see….
Example 1: Use a calculator to evaluate:
4.5 x 10-5
1.6 x 10-2
You must include parentheses
(4.5 x 10
-5)
(1.6 x 10
-2)
0.0028125
Write in scientific notation.
2.8125 x 10-3
Ex. 2: Use a calculator to evaluate:
7.2 x 10-9
1.2 x 102
On the calculator, the answer is:
6.E -11, E = exponent!!!
The answer in scientific notation is
6 x 10 -11
The answer in decimal notation is
0.00000000006
Ex. 3: 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
Ex. 4: Use a calculator to evaluate
(3,600,000,000)(23).
On the calculator, the answer is:
8.28 E +10, E = exponent
The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000
Ex. 5: Write (2.8 x 103)(5.1 x 10-7) in
scientific notation.
A. 14.28 x 10-4
B. 1.428 x 10-3
C. 14.28 x 1010
D. 1.428 x 1011
You Try, write in scientific and standard
notation
A) (5.3 x 102)(4.1 x 105)
B) (2 x 10-5)(9.4 x 10-3)
C) 1.5 x 102
2.5 x 1012
D) 1.25 x 104
2.5 x 10-6
You practice
• Find your textbook and practice page 429 #4455. Turn in for a CW grade.
• I should hear you talking and communicating
with each other!
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
Example 6) 234.6 x 109
2.346 x 1011
Example 7) 0.0642 x
4
10
on calculator: 642
6.42 x 10 2
Ex. 9: 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