Download Scientific Notation

Scientific Notation
-express numbers in scientific and
decimal notation.
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.
Part 1. 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 exponent
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
NOTE:
• If you are moving the decimal point to the
LEFT, the exponent will be POSITIVE!
• If you are moving the decimal point to the
RIGHT, the exponent will be NEGATIVE!
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
EXAMPLES…
write in scientific notation
•
•
•
•
1.
2.
3.
4.
3,725,000
0.000316
14,140,000
0.114
Part 2. Writing in
Standard Form
-if the problem is already written in
scientific notation, you will have to
write it in standard form
To write in standard form:
• Take the decimal point and move it the
number of spaces indicated by the exponent
Ex. 2.36 x 105…you will move the decimal
point 5 places
• If the exponent is POSITIVE, you will move
the decimal point to the RIGHT
• If the exponent is NEGATIVE, you will
move the decimal point to the LEFT
• Opposite of how you write it in scientific
notation
Write 3.27 x 10-3 in standard
notation.
1.
2.
3.
4.
327,000
3,270
0.0327
0.00327
2) Express 1.8 x 10-4 in decimal
notation.
0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
Rewriting problems into proper
scientific notation
• Sometimes, problems will be written in
improper scientific notation.
• In order to fix it, you have to move the
decimal into its proper location
• When that happens, you will have to add
onto the original exponent
Write 531.42 x 105 in scientific
notation.
531.42 x 105
Since you moved the decimal point 2 places to
the left, you add on 2 digits to the exponent
5.3142 x 107
Write 0.00042 x 108 in scientific
notation.
Since you moved the decimal point 4 places to
the right, you subtract 4 digits to the exponent
4.2 x 104