Scientific Notation: Converting, Multiplying, Dividing & More
TOPIC: Scientific Notation
•
The number is written as the
product
product
of two
other numbers:
–
A number between 1 and 10 (
not
not
10)
–
and
–
A power of 10
20.3 x 10
2
NOT CORRECT
2.03 x 10
3
CORRECT
Converting
conventional
conventional
to
to
scientific notation
scientific notation
For numbers
1
1
, the
exponent
exponent
will
be
positive
positive
. Count how many places
the decimal is moved.
329
3.29 X 10
2
Converting
conventional
conventional
to
to
scientific notation
scientific notation
For numbers
between 0 and 1
between 0 and 1
, the
exponent
exponent
will be
negative
negative
. Count
how many places the decimal is
moved.
0.00045
4.5 X 10
-4
Converting
scientific to
scientific to
conventional
conventional
notation
If the exponent is positive,
the number
1, so move the
decimal point right.
3.784 X 10
5
378400
Converting
scientific to
scientific to
conventional
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 10
a
) x (M x 10
b
) = (N x M) x 10
a+b
•
(5.1 x 10
4
) x (2.5 x 10
3
) = (5.1 X 2.5) x 10
(4+3)
•
(5.1 x 10
4
) x (2.5 x 10
3
) = 12.75 x 10
7
•
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 10
8
Dividing
•
(N x 10
a
) / (M x 10
b
) = (N / M) x 10
a-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
Scientific notation is a way to express large or small numbers efficiently. Learn how to convert numbers to and from scientific notation, multiply and divide in scientific notation, and ensure proper formatting. Understand the rules for exponents and make calculations easier with these simple steps.
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Presentation Transcript
TOPIC: Scientific Notation The number is written as the product of two other numbers: A number between 1 and 10 (not 10) and 20.3 x 102 NOT CORRECT A power of 10 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
