Scientific
Notation
The basics and some math.
Take out your calculator.

Write these calculations and the answer in
your notes:

12,922,341 / 0.011 435 7 =

1,130,000,000

0.05 / 20,111 =

0.000 002 486
Re-writing numbers in
SCIENTIFIC NOTATION
makes it so we don’t have
to deal with all of these
“extra” zeros.
What is it?
Scientific Notation
(Exponential Notation)
 Scientific
Notation is used to
express any number as:

a number between 1 and 10
 (called

multiplied by 10
 (the

a coefficient)
“base” as in “base 10”)
raised to a power
 (indicated
by an exponent)
coefficient = 9.13
8
9.13x10
9.13E8
exponent = 8
First, let’s review exponents
 10
= 10 (x 1)
= 101
 100 = 10 x 10
= 102
 1,000 = 10 x 10 x 10
= 103
 10,000 = 10 x 10 x 10 x 10 = 104
 The
Count the “0”s
1
2
3
4
number in the exponent tells you how many
times ten is multiplied by itself.
Reviewing Exponents
 Any
number raised to the 0
power – or has a 0 in the
exponent = 1.
 So,
100 = 1
Scientific Notation
Base 10 cont.
What does this really
mean?
 109
would equal a 1 followed by how many
zeros?
9
 1,000,000,000
 What
would 1.13 x 109 be if written in “long
form?”
 Move
the decimal place to the right 9 places.
 1,130,000,000
When you have a positive
exponent, move your
decimal to the right the
same number of places
that are in the exponent.
Let’s rewrite the first number we
calculated in scientific notation.
 12,922,341
/ 0.011 435 7 =
 1,130,000,000
 1.13
x 109
What does this really
mean?
Scientific Notation
Base 10 – negative exponents
 If
the exponent is negative, think division.
 10-1 =
1/(10)
= 0.1
 10-2 = 1/(10 x 10)
=1/(100)
= 0.01
 10-3 = 1/(10 x 10 x 10) = 1/(1,000)
= 0.001
 10-4 = 1/(10 x 10 x 10 x 10)= 1/(10,000) = 0.0001
Move the decimal point to
the left if you have a
negative exponent.
Let’s rewrite our second
number in scientific notation.
 0.05
/ 20,111 = 0.000 002 486
 Coefficient
= 2.486
 The decimal would have to be moved to
the left 6 places, so our exponent will be 6.
 2.486 x 10-6
Now give it a try with a
partner. You have 5 minutes.