Scientific Notation
Scientific Notation
What does the sun weigh?
4,400,000,000,000,000,000,000,000,000,000 lbs.
How much hydrogen does the
sun burn each second?
600,000,000 metric tons
Scientific Notation
How much longer will
the sun burn?
6,000,000,000 years.
Scientific Notation
Let’s look at these large
Numbers
4,400,000,000,000,000,000,000,000,000,000
lbs.
600,000,000 metric tons
6,000,000,000 years
Each of these numbers can be
written in a different form
called Scientific Notation
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
Scientific Notation
Scientific Notation is made up of 2
parts.
1st Part = a number between
1 and 9
2nd Part = x 10 to some power
If it doesn’t have both parts, it is
NOT Scientific Notation.
Scientific Notation
Let’s change these large
Numbers to Scientific
Notation…..
4,400,000,000,000,000,000,000,000,000,000
lbs.
4.4 x
30
10
lbs.
Place the decimal pt. after the
first # and then count to the
end.
Scientific Notation
600,000,000 metric tons
6.0 x 10?
6.0 x 108 metric tons
6,000,000,000 years
9
6.0 x 10 years
Change to Scientific Notation
1570
Place the decimal just after
the first number. 1.570
Then count the # of places
1570
= 1.57 x
3
10
Change to Scientific Notation
832,000,000
Place the decimal just
after the first number.
Then count the # of
places =8.32 x 108
832,000,000
Change to Scientific Notation
2450 =
3
2.45 x 10
765,000,000 =
8
7.65 x 10
0.000722
-4
= 7.22 x 10
Change to Scientific Notation
0.000722
Place the decimal just
after the first number.
Then count the # of
places. = 7.22 x 10-4
000722
Change to Standard Notation
Now let’s go backwards
and change from Scientific
Notation to Standard
Notation.
Change to Standard Notation
5
10
4.53 x
Move the decimal pt.
5 places to the right.
453000 = 453,000
Try this one
8.2 x 10-8
.000000082
Multiplying with Scientific
Notation
(2.5x102 )( 2.5x 103 )
Multiply the coefficients
2.5 x 2.5 = 6.25
Add the Exponents
102 + 103 = 105
Put it together
6.25 x105
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 + 103 = 105
7.59 X 105
Multiplying with Scientific Notation
(4.6 X 104) X (5.5 X 103) = ?
Answer 25.3 x 107
Correct answer = 2.53 x108
(3.1 X 103) X (4.2 X 105) = ?
Answer= 13.02 x 108
Correct Answer= 1.302 x 109
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
Put them together
1.43 X 102
Dividing with Scientific Notation
(4.6 X 104) / (5.5 X 103) = ?
Answer= 0.836x 101
Correct answer = 8.36
(3.1 X 103) / (4.2 X 105) = ?
Answer = .738x 10 -2
Correct answer =7.38x10-3