Transcript Scientific Notation

Scientific Notation
Scientific Notation
Objective: To identify
standard form and scientific
notation and be able to
convert from one to the
other with ease
Scientific Notation
What is standard form
notation?
It is how we normally write numbers …. How
we have always learned to write numbers
• 650
Examples anyone?
• 1,700,000
• 0.005
Scientific Notation
What is Scientific notation?
It is how scientists and engineers write
numbers … it is ideal for writing very big
numbers
Notice – there is only ONE number to the left
of the decimal point …. always
Here are
some
examples
• 6.5 • 102 (was 650)
• 1.7 • 106 (was 1,700,000)
• 5 • 10-3 (was 0.005)
Scientific Notation
How do you convert from
standard form to scientific
notation?
1,200 is standard form
1.2
 10
Positive exponent because
number was greater than 1
3
Count
Re-write
thethe
number
number
of
numbers
with just to
ONE
thenumber
right
of
to where
the leftthe
of decimal
the
went
decimal
… that
point
will be
the exponent
Scientific Notation
What is the number is less than
one
0.0012 is standard form
1.2  10
-3
Negative exponent because
number was less than 1
Count
thethe
number
of
Re-write
number
numbers
thenumber
left of
with just to
ONE
where
to the the
left decimal
of the
went
… that
will be
decimal
point
the exponent
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
750
7.5 •
2
10
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
1,250,000
1.25  10
6
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
7500
7.5  10
3
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
0.00015
1.5  10
4
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
1.25
1.25  10
0
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
0.0105
1.05  10
2
Scientific Notation
Let’s try some ….. Convert
these standard form numbers
to scientific notation
5,025,000
5.025  10
6
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
3 6
15.03
.025
 10
 10
5,025,000
0.00103
Look to see if the exponent is
positive or negative …. Positive
– move to right … neg move to
left (like a number line)
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
3.25 10
5
325,000
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
1.3  10
3
1,300
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
1.3 10
4
0.00013
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
7.503 10
2
750.3
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
2.7  10
6
0.0000027
Scientific Notation
Now, how do we convert back
from scientific notation to
standard form notation
8.013 10
4
80,130