Transcript Scientific Notation Notes

Scientific Notation
What is scientific Notation?
Scientific notation is a way of
expressing really big numbers or really
small numbers.
 It is most often used in “scientific”
calculations where the analysis must be
very precise.

Scientific notation consists of
three parts:

A number between 1 and 10 = coefficient
 The base number of 10
 An exponent
5.67 x
5
10
Changing scientific notation to
standard form.
To change scientific notation to
standard form…
Simply move the decimal point to the
right for a positive exponent.
 Move the decimal point to the left for
negative exponent.

(Use zeros to fill in places.)
Example 3
Given: 5.093 x 106
 Answer: 5,093,000 (moved 6 places to
the right)

Example 4
Given: 1.976 x 10-4
 Answer: 0.0001976 (moved 4 places to
the left)

Changing standard form to
scientific notation.
To change standard form to
scientific notation…
Place the decimal point so that there is
one non-zero digit to the left of the
decimal point.
 Count the number of decimal places the
decimal point has “moved” from the
original number. This will be the
exponent on the 10.

Continued…
If the original number was less than 1,
and you moved the decimal to the right,
then the exponent is negative.
 If the original number was greater than
1, and you moved the decimal to the
left, then the exponent is positive.

Example 1
Given: 289,800,000
 Use: 2.898 (moved 8 places)
 Answer: 2.898 x 108

Example 2
Given: 0.000567
 Use: 5.67 (moved 4 places)
 Answer: 5.67 x 10-4

Multiplying with Exponents
Multiply the base numbers together.
 Then add the exponents to get the
power of 10.
 General formula:

(N X 10x) (M X 10y) = (N) (M) X 10x+y
Example 3
Given: (3.45 X 107)(6.25 X 105)
 Multiply bases: 3.45 X 6.25 = 21.5625
 Add Exponents: 107+105=107+5=1012
 Answer: 21.5625 X 1012
 Shift Decimal left one place.
 Final Answer: 2.15625 X 1013

Dividing with Exponents
Divide the base numbers.
 Then subtract the exponents to get the
power of 10.
 General formula:

N X 10x / M X 10y = N/M X 10x-y
Example 4
Given:8 X 10-3 / 2 X 10-2
 Divide bases: 8/2=4
 Subtract exponents: (-3)-(-2)=-1
 Answer: 4 X 10-1

Adding/Subtracting
When adding or subtracting numbers in
scientific notation, the exponents must
be the same.
 If they are different, you must move the
decimal either right or left so that they
will have the same exponent.

Moving the decimal
For each move of the decimal to the
right you have to subtract 1 from the
exponent.
 For each move of the decimal to the left
you have to add 1 to the exponent.
 It does not matter which number you
decide to move the decimal on, but
remember that in the end both numbers
have to have the same exponent on the
10.

Example 5
Given: 3.76 X 104 + 5.5 X 102
 Shift decimal 2 places to the left for 104.
 Move: .055 X 102+2
 Add: 3.76 X 104 + .055 X 104
 Answer: 3.815 X 104

Example 6
Given: 4.8 X 105 – 9.7 X 104
 Shift decimal 1 places to the left for 105.
 Move: .97 X 10(4+1)
 Subtract: 4.8 X 105-.97 X 105
 Answer: 3.83 X 105
