Transcript Scientific Notation

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
An ordinary penny contains about
20,000,000,000,000,000,000,000 atoms. The average
size of an atom is about 0.00000003 centimeters
across.
The length of these numbers in
standard notation makes them
awkward to work with.
Scientific notation is a shorthand way of writing such
numbers.
In scientific notation the number of atoms in a penny is
2.0  1022, and the size of each atom is 3.0  10–8
centimeters across.
Helpful Hint
The sign of the exponent tells which direction to
move the decimal. A positive exponent means move
the decimal to the right, and a negative exponent
means move the decimal to the left.
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
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
Additional Example 1A: Translating Scientific
Notation to Standard Notation
Write the number in standard notation.
A. 1.35  105
1.35  10
5
105= 100,000
1.35  100,000
135,000
Since the exponent is a positive 5 move to the
right 5 spaces. You move to the right when the
exponent is positive because the number must
be greater than 1 when the exponent is positive.
Additional Example 1B: Translating Scientific
Notation to Standard Notation Continued
Write the number in standard notation.
B. 2.7  10
–3
2.7  10
–3
10 –3
1
2.7 
100

100
2.7
0.0027
=
1
100
Divide by the reciprocal.
Think: Move the decimal left 3 places. Move to
the left to make the number less than one since
the exponent is negative, move three places
because the exponent is 3.
Lesson Quiz
Write in standard notation.
1. 1.72  104
17,200
2. 6.9  10–3
0.0069
Write in scientific notation.
3. 0.0053
5.3  10–3
4. 57,000,000
5.7  107
5. A human body contains about 5.6 x 106 microliters
of blood. Write this number in standard notation.
5,600,000
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
8) 234.6 x 109
2.346 10
92
Move the decimal two places.
Since the number was greater
than 1 add 2 to the exponent
2.346 10
11
9) 0.0642 x 104
6.42 10 42
6.42 10
2
Move the decimal two
places. Since the number is
less than 1 subtract 2 from
the exponent
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
Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103)
•
Multiply the Coefficients
•
2.3 X 3.3 = 7.59
•
Add the Exponents
•
102 X 103 = 105
•
7.59 X 105
•
759,000
Multiplying with Scientific Notation
• (4.6 X 104) X (5.5 X 103) = ?
25.3 10
7
2.53 10
8
This is not in proper scientific
notation, so get in in the correct
form. Remember since you
moved one place and the
number was greater than 1 add it
to the exponent.
• (3.1 X 103) X (4.2 X 105) = ?
13.02 10
9
1.302 10
8
This is not in proper
scientific notation, so get in
in the correct form.
Remember since you moved
one place and the number
was greater than 1 add it to
the exponent.
Dividing with Scientific Notation
• (3.3 X 104)/ (2.3 X 102)
• Divide the Coefficients
• 3.3/ 2.3 = 1.434783
• Subtract the Exponents
• 104 / 102 = 102
• 1.4347823 X 102
• 143.4783

Dividing with Scientific Notation
4.6 10
2
5.5 10
4
.8363636364 10 2
8.3636364 10
1
3.110 3
4.2 10 5
.7380952381102
7.380952381103
Since the answer is not in proper form,
you must get it in proper form. The
decimal must be moved one place.
Since the number is less than one, you
must subtract 1 from the exponent 2
Since the answer is not in proper form,
you must get it in proper form. The
decimal must be moved one place.
Since the number is less than one, you
must subtract 1 from the exponent -2
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 standard notation is
0.00000000006
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 standard 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