Chemistry Reference
In-Depth Information
Solution
(a)
The decimal point must be moved two places to the
left,
so the exponent
is
increased
by
10
6
.
2: 2.37
Read the instruction manual for
your calculator to learn to
change numbers in decimal
format to scientific notation.
(b)
The decimal point has to be moved two places to the
right,
so the
exponent is
reduced
by
10
3
.
2: 1.41
10
2
(c)
The coefficient is reduced by a factor of 100 (equal to
), and the
10
2
exponential part is increased by the same factor:
3.003
.
Practice Problem 2.11
Change the format of each of the following
numbers to scientific notation:
(a)
10
7
10
3
10
1
0.0110
(b)
240
(c)
0.000123
Multiplication and Division of Exponential
Numbers
To multiply numbers in exponential format, we multiply the coefficients and the
exponential parts separately. To multiply exponential parts, the exponents are
added.
For example, let's multiply
10
3
10
4
:
4.0
and
1.5
10
3
)
10
4
)
(10
3
10
4
)
(4.0
(1.5
(4.0
1.5)
10
3
4
10
7
6.0
6.0
It's easy to see that if we multiply three tens by four tens, we get seven tens:
10
3
10
4
(10
10
10)
(10
10
10
10)
10
7
10
10
10
10
10
10
10
EXAMPLE 2.12
Multiply the following numbers, and express the answers in scientific notation:
(a)
(b)
(c)
10
3
)
10
4
)
(2.0
(3.0
10
3
)
10
5
)
(4.0
(5.0
10
7
)
10
4
)
(6.0
(1.5
Solution
10
3
)
10
4
)
10
7
(a)
(b)
(c)
(2.0
(3.0
6.0
10
3
)
10
5
)
10
8
10
9
(4.0
(5.0
20
2.0
10
7
)
10
4
)
10
11
(6.0
(1.5
9.0
Practice Problem 2.12
Multiply the following numbers and express
the answers in scientific notation:
(a)
(b)
(c) (2.0
10
7
)
10
7
)
(4.5
(4.0
10
3
)
10
4
)
(6.0
(3.5
10
8
)
10
7
)
(2.7
