Transcript Exponential Notation or Scientific Notation

Exponential Notation or Scientific Notation
Why do we use it?

To better express very large or very small numbers
How are exponential notation and
scientific notation similar?
There
is a digit term and an exponential term with both
How are exponential notation and
scientific notation different?
•Scientific notation’s digit term is always greater than or equal to
1 and less than 10
Rule #1  Addition and Subtraction when using exponents

You must make the exponents the same
Ex.
3.1 x 102 g +
1.9
x 104 g
Must be equal


Choose either number to change the exponent
How? Move the decimal in the digit term to change the exponent
Ex. 1.9 x 104 g  to change the exponent from 104 to 102, move the
decimal 2 times in the digit term
1.9  190
by doing this, you now have an exponential term of 102 and the number
representation of …
190 x 102 g

Rule of thumb:



When moving the decimal in the digit term
Left is Larger
Right is Reducing
This is what happens to the
exponent!
Addition and Subtraction cont.

Now add (or subtract) the numbers as the
numbers now have the same exponent
Ex. 3.1 x 102 g
+
190 x 102 g
193.1 x 102 g

Change to scientific notation if not
already in scientific notation
Multiplication and Division
Rule #2  Multiplication and Division when using exponents

When multiplying…
 Add exponents
(3.0 x 102 m) (2.0 x 105 m)
 6.0 x 107 m2

When dividing…

Subtract exponents
6.0 x 103 g
2.0 x 101 mL
 3.0 x 102 g/mL