Transcript Scientific Notation

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• What do the numbers to the
left have in common?
• They all start with a number
between 1 and 10
• They are all multiplied by the
base power of 10
• They all have exponent
• They describe numbers that
are generally very large or
very small
• 2.898 x 10-4
• 5.670 x 108
6
• 5.093 x 10
-3
• 2.8125 x 10 • They are written in
scientific notation
• 9.0 x 10-7
Common Core Numbers
5&6
• Express large and small
numbers in scientific
notation including use in
real-world problems
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
One way people use scientific 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.
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
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
NOTEBOOK EXAMPLES
Express 0.00018in scientific notation.
1.8 x 10-4
Express 4,580,000 in scientific notation.
4.58 x 106
Changing Numbers from Scientific
Notation to Standard Notation
Lets take 5.67 x 108 which is written in
scientific notation. You want to know the
actual number. So lets change it into
standard form.
You move your decimal 8 places to the right
filling in zeros where you have no numbers.
(See board for example)
The final answer would be 567,000,000
Changing Numbers from Scientific
Notation to Standard Notation
Lets take 2.367 x 10-4 which is written in
scientific notation. You want to know the
actual number. So lets change it into
standard form.
You move your decimal 4 places to the left
filling in zeros where you have no numbers.
(See board for example)
The final answer would be 0.0002367
You try a few! Write the numbers
in standard form.
• (1) 2.093 x 106
• (2) 2.8125 x 10-3
• (3) 9.0 x 10-7
•
•
•
•
ANSWERS
(1) 2,093,000
(2) 0.0028125
(3) 0.0000009
Comparing Numbers
• Which is larger?
(A) 4.67 x 10-4
(C) 4/10,000
(B) 0.00046
(D) 4.7 x 10-5
• The answer is (A) 4.67 x 10-4
• How did you figure it out?
• You could have written your answers in standard
notation or just know -4 is bigger than -5 on the
number line
PRACTICE PROBLEMS
• Pages 102
• 1-10
• You will have to
apply your
knowledge on #9