Perform the division and express the result in scientific notation:

[tex]\[
\frac{6.8 \times 10^{-4}}{2.5 \times 10^2}
\][/tex]

Select one:
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]



Answer :

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]