Download Scientific Notation

Scientific Notation
Ch. 3
Scientific Notation
• We use scientific notation because we deal with
very large and very small numbers.
• Scientific notation is written as a product of 2
numbers. The first is a coefficient, and the second
is 10 raised to a power called an exponent.
Coefficient is always a number greater
than 1 and less than 10.
The exponent equals the number of places
the original decimal point has been moved to write
in scientific notation.
Scientific Notation
• When moving the decimal to the left, the
exponent is positive
Ex. 1
36,000 is written as 3.6 X 104
• When moving the decimal to the right, the
exponent is negative
Ex. 2
0.0081 is written as 8.1 X 10-3
Multiplying using scientific notation
• To multiply, simply multiply the coefficients
and add the exponents
Ex. (3.0 X 104) x (2.0 X 102)
(3.0 x 2.0) X 10 4+2
6.0 X 106
Dividing using scientific notation
• To divide, simply divide the coefficients and
subtract the exponents.
• Ex. (3.0 X 104) / (2.0 X 102)
(3.0 / 2.0) X 10 4-2
1.5 X 102
Addition or subtraction using scientific
notation
• To add or subtract, the exponents must be
made to be the same. This is like lining up the
decimal when we add or subtract.
Ex. (5.40 X 103) + (6.0 X 102)
First, make the exponent the same
(5.40 X 103) + (.60 X 103)
Now just add or subtract the coefficients
(5.4 + .60) X 103 = 6.0 X 103