Transcript Scientific Notation

Today’s Objective
•To be able to express
a very large number
or very small number
in 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
• Scientific Notation is made
up of 2 parts.
• 1st Part = a number between
1 and 10
• 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.
30
10
• 4.4 x
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
8
• 6.0 x 10 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 103
Change to Scientific Notation
•832,000,000
•Place the decimal just after
the first number.
•Then count the # of places
8
•832,000,000 =8.32 x 10
Change to Scientific Notation
3
10
• 2450 = 2.45 x
8
• 765,000,000 = 7.65 x 10
-4
• 0.000722 = 7.22 x 10
Notice that if the decimal moves
right the exponent is negative
and if it moves left, the decimal
is positive.
Change to Scientific Notation
•0.000722
•Place the decimal just after
the first number.
•Then count the # of places.
-4
•000722 = 7.22 x 10
Change to Standard Notation
•Now let’s go backwards
and change from
Scientific Notation to
Standard Notation.
Change to Standard Notation
•4.53 x
•Move the decimal pt. 5
places to the right.
•453000 = 453,000
5
10
Scientific Notation
3
5
•(5 x 10 )(4 x 10 )
•5 x 4 = 20
3
5
8
•10 x 10 = 10
Now convert to
8
•20 x 10 Scientific Notation
9
2.0 x 10
Try this one
•820,000,000
8.2 Place the point after the 1st #
Count to the end
8.2 x
8
10
Try this one
2
7
•(6 x 10 )(3 x 10 )
•6 x 3 = 18
2
7
9
•10 x 10 = 10
Now convert to
9
•18 x 10 Scientific Notation
10
1.8 x 10
Try this one
3
2
10 )
•(5 x
=
3
3
•(5 x 10 ) (5 x 10 )
•5 x 5 = 25
3
3
6
•10 x 10 = 10
•25 x
6
=
10
2.5 x
7
10