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Scientific Notation Notes
The Mall of America is Bloomington, Minnesota, is the largest shopping
and entertainment center in the United States. The table shows two
features of the mall.
Standard
Form
Number of
Parking
Spaces
Area of Mall
(square feet)
Abbreviated
Form
Product of a
number and a
power of ten
13 thousand
13 x 1,000
Product of a
number and a
power of ten
using exponents
4,200,000
 A number is in ______________________________
when it is written as the product of a number and a power
of ten.
EXAMPLES: 60,000 = 6.0 x 104
3,500,000,000 = 3.5 x 109
 The number MUST be ________________________ to 1
and ___________________ 10.
EXAMPLES: Circle the numbers written in scientific notation.
45.6 x 103
2.3 x 1024
333.7 x 102
5.6 x 1012
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1. To write a number in STANDARD FORM you apply the
order of operations:
First, evaluate the power of ten and then multiply.
 A shortcut would be to move the decimal to the right the
same amount of times as the ____________ of ten (or as
the number of zeros.)
EXAMPLE:
5.2 x 104
5.2 x 104
=
=
5.2 x 104
=
5.2 x 10,000
move the decimal point 4
places to the right
52,000
YOUR TURN: Write Each Number in Standard Form
a. 7.2 x 104
b. 3.8 x 109
c. 1.0 x 108
2. To write a number in SCIENTIFIC NOTATION:
First, move the decimal point to right of the first
digit and then find the power of ten by counting the number of
places moved.
EXAMPLE: Write 42,500 in scientific notation.
 42,500 has to be put into a number that is between 1 and 10
The greatest place value is the ones place.
 The decimal would have to be moved 4 times to get a
number between 1 and 10.
 Once you have a number between 1 and 10 you can get rid of
the last zeros.
42,500 = 4.2500 x 10,000 = 4.2500 x 104 = 4.25 x 104
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YOUR TURN: Write each number in scientific notation.
23,500,000 = ______________________________________
38,000,000 = ______________________________________
19,000 = __________________________________________
86.1 billion = _______________________________________
WRITING: Explain why scientific notation is used with large
numbers.
_________________________________________________
_________________________________________________
_________________________________________________
NUMBER SENSE: Which number describes the population of
Chicago, 3.0 x 106 or 3.0 x 103? Explain your reasoning.
_________________________________________________
_________________________________________________
_________________________________________________
PLANETS: The average distance between Earth and the Sun is
92,960,000 miles. Write this distance in scientific notation.
_________________________________________________
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