Scientific Notation

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TOPIC: Scientific Notation
• The number is written as the product of two
other numbers:
– A number between 1 and 10 (not 10)
– and
– A power of 10
20.3 x 102 NOT CORRECT
2.03 x 103 CORRECT
Converting conventional to
scientific notation
For numbers  1, the exponent will
be positive. Count how many places
the decimal is moved.
329

3.29 X 102
Converting conventional to
scientific notation
For numbers between 0 and 1, the
exponent will be negative. Count
how many places the decimal is
moved.
0.00045

4.5 X 10-4
Converting scientific to
conventional notation
If the exponent is positive,
the number  1, so move the
decimal point right.
3.784 X 105

378400
Converting scientific to
conventional notation
If the exponent is negative, the
number is between 0 and 1 so move
the decimal point to the left.
2.75 X 10-3

0.00275
Multiplying
•
•
•
•
(N x 10a) x (M x 10b) = (N x M) x 10a+b
(5.1 x 104) x (2.5 x 103) = (5.1 X 2.5) x 10(4+3)
(5.1 x 104) x (2.5 x 103) = 12.75 x 107
Oops – new answer isn’t scientific notation
– Remember has to be between 1 and 10
– 12.75 = 1.275
– since we made the number smaller we have to
make the exponent bigger
– 1.275 x 108
Dividing
•
•
•
•
(N x 10a) / (M x 10b) = (N / M) x 10a-b
(3.66 x 10-5) / (2.0 x 10-3) = (3.66/2.0) x 10(-5-(-3))
= 1.83 x 10-5+3
=1.83 x 10-2
• Write this as a normal number
.0183
Adding/Subtracting
• Exponents must be same number
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