To solve the problem and determine the correct numerical result, let's go through the detailed steps involved in solving the given expression. The goal is to divide the numerator [tex]\(2.4 \times 10^8\)[/tex] by the denominator [tex]\(5 \times 10^{-6}\)[/tex].
### Step-by-Step Solution
#### Step 1: Understand the Notation
We need to divide two numbers written in scientific notation:
[tex]\[
\frac{2.4 \times 10^8}{5 \times 10^{-6}}
\][/tex]
#### Step 2: Divide the Numerical Coefficients
First, divide the coefficients (the numbers in front of the powers of 10):
[tex]\[
\frac{2.4}{5} = 0.48
\][/tex]
#### Step 3: Subtract the Exponents
When dividing numbers in scientific notation, we subtract the exponent of the denominator from the exponent of the numerator:
[tex]\[
10^8 \div 10^{-6} = 10^{8 - (-6)} = 10^{8 + 6} = 10^{14}
\][/tex]
#### Step 4: Combine the Results
Combine the result of dividing the coefficients with the result of subtracting the exponents:
[tex]\[
0.48 \times 10^{14}
\][/tex]
This can be rewritten for clarity as:
[tex]\[
4.8 \times 10^{13}
\][/tex]
#### Step 5: Verify Against Possible Answers
Now, let's check this result against the given possible options:
- [tex]\(4.8 \times 10^{13}\)[/tex]
- [tex]\(0.48 \times 10^{14}\)[/tex]
- [tex]\(4.8 \times 10^1\)[/tex]
- [tex]\(4.8 \times 10^{15}\)[/tex]
We see that:
[tex]\[
0.48 \times 10^{14} = 4.8 \times 10^{13}
\][/tex]
and both match our solution.
Therefore, the correct numerical result is:
[tex]\[
4.8 \times 10^{13}
\][/tex]
### Summary of the Given Answer
Given the result:
[tex]\[
(48000000000000.01, 48000000000000.0, 48000000000000.0, 48.0, 4800000000000000.0)
\][/tex]
It corresponds to:
[tex]\[
4.8 \times 10^{13}
\][/tex]
Thus, the step-by-step method verifies the correct solution to the initial mathematical expression.
