Scientific Notation
or
Exponential Notation
Summer 2007
Purposes
„
To write very large and very small
numbers
602000000000000000000000 =
6.02 X 1023
0.00000000000000000000247 =
2.47 X 10-21
The Mole, mol
„
„
Unit of quantity – always the same
6.02 X 10 23
one mol of Zinc is 6.02 X 10 23 zinc atoms
Note CHEM 1406: Add mole to Table 1.1,
page 2 of textbook
Purposes
„ Mathematical
operations with very
large and very small numbers
(7.11 X 1018/9.05 X 10-7) =
0.786 X 1025 =
7.86 X 1024
Writing Numbers
„ Form:
power
Number X 10
Number between 1 and 10
+ power value – original number
greater than 1
- power value – original number
less than 1
examples
„ 1205000000
„
9
1.205 X 10
300087.
5
3.00087 X 10
Number X 10power
Number portion is
between 1 and 10
Power portion is
positive number
examples
„ 0.0000318
„
-5
3.18 X 10
0.0000000040
-9
4.0 X 10
Number X 10power
Number portion is
between 1 and 10
Power portion is
negative value
Practice Examples
„ 0.00000000000000000003500
„ 3.500
-20
X 10
„ 2570600000000000
„ 2.5706
15
X 10
is
is
Multiplication
„ For
multiplication the exponents are
added
A
B
(10 )(10 ) = 10(A + B)
7
18
5
-11
(10 ) (10
(10 ) (10
) = 10(7 + 18)
) = 10(5 - 11)
25
= 10
-6
= 10
Multiplication Example
„ (4.13
7
12
x10 ) (2.70 x10 ) =
7
12
(4.13)(2.70) X (10 )(10 ) =
7 + 12
11.151 x (10
)=
19
11.151 x (10 ) =
1
19
1.1151 x 10 x 10 =
20
1.12 x 10
Multiplication Example
„ (6.1
-7
12
x10 ) (8.47 x10 ) =
-7
12
(6.1)(8.47) X (10 )(10 ) =
-7 + 12
51.667 x (10
)=
5
51.667 x (10 ) =
1
5
5.1667 x 10 x 10 =
6
5.2 x 10
Division
„
For division, the exponent from the
denominator is subtracted from the
exponent of the nominator
X
Z
X–Z
(10 )/ (10 ) = (10
8
15
)
8 –15
(10 )/ (10 ) = (10
-7
) = 10
Division Example
„ (7.003
11
20
-9
-9
x 10 )/ (5.6 x 10 ) =
(11 – 20)
=
(7.003)/(5.6) x 10
1.2505 x 10 = 1.3 x 10
Division Example
„ (4.18
11
-9
x 10 )/ (8.005 x 10 ) =
(11 – (-9) )
=
(4.18)/(8.005) x 10
(11 +9)
0.52217 x 10
=
20
0.52217 x 10 =
-1
20
19
5.22 x 10 x 10 = 5.22 x 10
(2.36 x 10-5)(7.003 x 1011)÷ (8.4 x 10-8) =
( -5 + 11 – (-8) )
(2.36)(7.003) X 10
=
(8.4)
( -5 + 11 +8 )
1.96751 x 10
=
( -5 + 19 )
1.96751 x 10
=
14
1.9675 x 10
14
= 2.0 x 10
Web Site
„
„
Site with examples, problems and answer key:
http://academic.cuesta.cc.ca.us/jpandosh/m23o
lf00/scinot/act3.htm
Online Solver – Scientific Notation:
http://www.math.com/students/solvers/numb
ers/scientificnotation.htm