Chemistry Reference
In-Depth Information
To divide exponential numbers, we divide the coefficients and the expo-
nential parts separately. To divide exponential parts, we subtract the exponents.
EXAMPLE 2.13
10
6
10
3
.
Divide
7.0
by
3.5
Solution
10
6
)/(3.5
10
3
)
10
6
3
10
3
(7.0
(7.0/3.5)
2.0
We can see that this procedure is correct:
10
6
7.0
7.0
10
10
10
10
10
10
10
3
3.5
10
10
10
3.5
10
3
2.0
10
10
10
2.0
10
4
10
2
Practice Problem 2.13
Divide
1.6
by
6.4
.
We can apply this procedure to calculate the quotient of two exponential
numbers even when the denominator has a larger magnitude than the numera-
tor. For example, let's divide
10
5
10
7
.
8.0
by
4.0
The rule for dividing
exponential numbers gives the following result:
10
5
)/(4.0
10
7
)
10
5
7
10
2
(8.0
2.0
2.0
What does the negative exponent mean? Writing out all the expressions enables us
to see:
10
5
8.0
8.0
10
10
10
10
10
10
7
2.0
10
10
10
10
10
10
10
4.0
1
10
2
2.0
a
b
0.020
2.0
10
10
The negative exponent means to
divide
the coefficient by the base a certain num-
ber of times.
EXAMPLE 2.14
10
3
)/(5.0
10
3
).
Calculate the quotient of
(9.5
Solution
By the rule for division of exponential numbers:
10
3
9.5
A positive exponent indicates
that the exponential part of the
number is greater than 1, a neg-
ative exponent indicates that it is
less than 1, and a zero exponent
indicates that it is equal to 1.
10
0
1.9
10
3
5.0
By cancellation:
10
3
9.5
9.5
10
10
10
1.9
10
3
5.0
5.0
10
10
10
