5.4 Scientific Notation
• Goals: To write a number that is in
standard notation in scientific notation
Scientific Notation
a shortcut for very large/small numbers
• The distance from earth to the north
star is 10,000,000,000,000,000,000
meters.
• Fewer errors if we write as 1.0 x 1019 ?
Given a # in Standard Notation write
it in Scientific Notation
1. Move decimal until the # is 1 ≤X <10
2. Then mult. that # by 10 to a power
3. The power will be the # of times you
moved the decimal (if u moved to the rt
it’s a neg. exp. If u moved to the lft it is a
positive exp.)
In short….
• Decimals ( between 0 and 1) have negative
exponents on the base of 10
• Numbers that are larger than 1 have positive
exponents on the base of 10
Scientific Notation
Write an equivalent expression
using scientific notation:
3,200
3.2  103
Must be at least 1.0 and
no more than 9.9999…
Scientific Notation
Write an equivalent expression
using scientific notation:
0.0307
3.07  10-2
Must be at least 1.0 and
no more than 9.9999…
5.4 Scientific Notation
• Goals: To write numbers that are in
scientific notation in standard notation
Change from scientific notation to
standard form:
move the decimal the same amt of times as the exp.
(if the exp + move to the right and if the exp is –
move to the left)
1.25 x
1250
3
10
Change from scientific notation
to standard form:
7.0 x
5
10
700,000
Change from scientific notation
to standard form:
4.8 x
-3
10
0.0048
Change from scientific notation
to standard form:
1.8 x
-4
10
0.00018
Homework
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