Download Scientific Notation

Scientific Notation
 Learning Targets:
 12. I can determine which numbers in a
measurement are significant and use these
rules to make precise calculations.
 13. I am able to convert values from
standard form into scientific notation and
vise-versa
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.
2.1 x 1023
When using Scientific Notation, there are
two kinds of exponents: positive and
negative
Positive Exponent:
2.35 x 108
Negative Exponent:
3.97 x 10-7
An easy way to remember this is:
• If an exponent is positive, the number
gets larger, so move the decimal to
the right.
• If an exponent is negative, the
number gets smaller, so move the
decimal to the left.
When changing scientific notation to
standard notation, the exponent tells you
how you should move the decimal:
With a positive exponent, move the
decimal to the right:
4.08 x 103 = 4 0 8
Don’t forget to fill in your zeroes!
The exponent also tells how many spaces
to move the decimal:
4.08 x 103 = 4 0 8
In this problem, the exponent is +3, so
the decimal moves 3 spaces to the right.
When changing scientific notation to
standard notation, the exponent tells you
how you should move the decimal:
With a negative exponent, move the
decimal to the left:
4.08 x 10-3 =
408
Don’t forget to fill in your zeroes!
The exponent also tells how many spaces
to move the decimal:
4.08 x 10-3 =
408
In this problem, the exponent is -3, so the
decimal moves 3 spaces to the left.
Try changing these numbers from
Scientific Notation to Standard Notation:
1) 9.678 x 104
96780
2) 7.4521 x 10-3
.0074521
3) 8.51 x 107
85,100,000
4) 4.09 x 10-5
.0000409
When changing from Standard Notation
to Scientific Notation:
1) First, write only the sig figs in the number. Move
the decimal after the first sig fig:
3258
2) Second, add your multiplication sign and
your base (10).
3 . 2 5 8 x 10
3) Count how many spaces the decimal moved
and this is the exponent.
3 . 2 5 8 x 10 3
3 2 1
When changing from Standard Notation
to Scientific Notation:
4) See if the original number is greater than or
less than one.
– If the number is greater than one, the
exponent will be positive.
348943 = 3.48943 x 105
– If the number is less than one, the
exponent will be negative.
.0000000672 = 6.72 x 10-8
Try changing these numbers from
Standard Notation to Scientific Notation:
1) 9,070,000
9.07 x 106
2) .0000345
3.45 x 10-5
3) .08376
8.376 x 10-2
4) 5,670
5.67 x 103
Scientific Notation Math
Multiplication
- multiply the numbers, add the indices
1.2 x 104 multiplied by 5 x 106 =
Division
- divide the numbers, subtract the indices
5.5 x 108 divided by 1.1 x 102 =
Convert the following numbers
between standard form and scientific
notation:
329
1.7 x 103
700,000
2.4503 x 105
20090
0.000034
0.01023
123.4
45.607
7.9 x 1011
2.8 x 10-3
7.45 x 10-1
2.3 x 10-7
Convert the following numbers/sums
into correct scientific notation:
3.59 x 103
3,590
5.56 x 106
5,560,000
2.2 x 10-3
0.0022
3.48 x 10-4
0.000348
1.805 x 105
180,500
3.04 x 10-7
0.000000304
On a Calculator
10X
• Locate these buttons: ^ , 2nd , LOG ,
• Scientific  Standard given 1.2 x 105
– 1.2 x 10
5 = 120,000
^
10X
– 1.2 2nd
LOG
5 = 120,000
• Standard  Scientific
given 120,000
Sci/Eng
– 120,000 =
DRG
select Sci =
Sci/Eng
– To undo: DRG select Flo =
Sci/Eng
DRG