Answer :
Let's solve the given expression step-by-step to find which option is equivalent.
The expression given is:
[tex]\[
\frac{(12 \times 10^2) - (7 \times 10^2)}{(8 \times 10^5)}
\][/tex]
1. Calculate the Numerator:
[tex]\((12 \times 10^2) - (7 \times 10^2)\)[/tex]
- First, compute [tex]\(12 \times 10^2 = 1200\)[/tex].
- Then, compute [tex]\(7 \times 10^2 = 700\)[/tex].
- Subtract these results: [tex]\(1200 - 700 = 500\)[/tex].
So, the numerator is [tex]\(500\)[/tex].
2. Calculate the Denominator:
[tex]\((8 \times 10^5)\)[/tex]
This is simply [tex]\(800,000\)[/tex].
3. Form the Fraction and Simplify:
Now, form the fraction using the calculated numerator and denominator:
[tex]\[
\frac{500}{800,000}
\][/tex]
Divide the numerator by the denominator:
[tex]\[
\frac{500}{800,000} = 0.000625
\][/tex]
4. Convert the Result to Scientific Notation:
The result [tex]\(0.000625\)[/tex] can be written in scientific notation. To express it, move the decimal point four places to the right:
[tex]\[
0.000625 = 6.25 \times 10^{-4}
\][/tex]
5. Find the Equivalent Expression:
Comparing with the choices given:
- A. [tex]\(6.25 \times 10^{-4}\)[/tex]
- B. [tex]\(6.25 \times 10^{-1}\)[/tex]
- C. [tex]\(6.25 \times 10^5\)[/tex]
- D. [tex]\(6.25 \times 10^4\)[/tex]
The equivalent expression for the fraction is [tex]\(6.25 \times 10^{-4}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{A}\)[/tex].
The expression given is:
[tex]\[
\frac{(12 \times 10^2) - (7 \times 10^2)}{(8 \times 10^5)}
\][/tex]
1. Calculate the Numerator:
[tex]\((12 \times 10^2) - (7 \times 10^2)\)[/tex]
- First, compute [tex]\(12 \times 10^2 = 1200\)[/tex].
- Then, compute [tex]\(7 \times 10^2 = 700\)[/tex].
- Subtract these results: [tex]\(1200 - 700 = 500\)[/tex].
So, the numerator is [tex]\(500\)[/tex].
2. Calculate the Denominator:
[tex]\((8 \times 10^5)\)[/tex]
This is simply [tex]\(800,000\)[/tex].
3. Form the Fraction and Simplify:
Now, form the fraction using the calculated numerator and denominator:
[tex]\[
\frac{500}{800,000}
\][/tex]
Divide the numerator by the denominator:
[tex]\[
\frac{500}{800,000} = 0.000625
\][/tex]
4. Convert the Result to Scientific Notation:
The result [tex]\(0.000625\)[/tex] can be written in scientific notation. To express it, move the decimal point four places to the right:
[tex]\[
0.000625 = 6.25 \times 10^{-4}
\][/tex]
5. Find the Equivalent Expression:
Comparing with the choices given:
- A. [tex]\(6.25 \times 10^{-4}\)[/tex]
- B. [tex]\(6.25 \times 10^{-1}\)[/tex]
- C. [tex]\(6.25 \times 10^5\)[/tex]
- D. [tex]\(6.25 \times 10^4\)[/tex]
The equivalent expression for the fraction is [tex]\(6.25 \times 10^{-4}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{A}\)[/tex].
