To solve the given problem, let's perform the division step-by-step and express the result in scientific notation.
### Step-by-Step Solution:
1. Write the given values:
[tex]\[
\text{Numerator} = 6.8 \times 10^{-4}
\][/tex]
[tex]\[
\text{Denominator} = 2.5 \times 10^2
\][/tex]
2. Perform the division:
[tex]\[
\frac{6.8 \times 10^{-4}}{2.5 \times 10^2}
\][/tex]
3. Separate the numeric and exponential parts for clearer calculation:
[tex]\[
\frac{6.8}{2.5} \times \frac{10^{-4}}{10^2}
\][/tex]
4. Calculate the division of the numerical parts:
[tex]\[
\frac{6.8}{2.5} = 2.72
\][/tex]
5. Calculate the division of the exponential parts:
Using the property of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{10^{-4}}{10^2} = 10^{-4-2} = 10^{-6}
\][/tex]
6. Combine the results of the numerical and exponential parts:
[tex]\[
2.72 \times 10^{-6}
\][/tex]
7. Express the result in scientific notation:
The final result of the division is:
[tex]\[
2.72 \times 10^{-6}
\][/tex]
Now, we need to select the correct answer from the given choices:
a. [tex]\(2.72 \times 10^6\)[/tex]
b. [tex]\(2.72 \times 10^{-6}\)[/tex]
c. [tex]\(1.7 \times 10^{-1}\)[/tex]
d. [tex]\(2.72 \times 10^{-2}\)[/tex]
The correct answer is:
b. [tex]\(2.72 \times 10^{-6}\)[/tex]
