College

An expression is shown:

[tex]\[
\frac{\left(12 \times 10^2\right) - \left(7 \times 10^2\right)}{\left(8 \times 10^5\right)}
\][/tex]

Which expression is equivalent?

A. [tex]6.25 \times 10^{-4}[/tex]

B. [tex]6.25 \times 10^{-4}[/tex]

C. [tex]6.25 \times 10^5[/tex]

D. [tex]6.25 \times 10^4[/tex]

Answer :

We start with the expression

[tex]$$
\frac{\left(12 \times 10^2\right) - \left(7 \times 10^2\right)}{8 \times 10^5}.
$$[/tex]

Step 1. Calculate the numerator

Calculate each term in the numerator:

- For the first term:
[tex]$$12 \times 10^2 = 12 \times 100 = 1200.$$[/tex]
- For the second term:
[tex]$$7 \times 10^2 = 7 \times 100 = 700.$$[/tex]

Subtract the second term from the first:

[tex]$$
1200 - 700 = 500.
$$[/tex]

So, the numerator is [tex]$500$[/tex].

Step 2. Calculate the denominator

The denominator is given as:

[tex]$$
8 \times 10^5 = 8 \times 100000 = 800000.
$$[/tex]

Step 3. Form the fraction

Now, substitute the calculated numerator and denominator into the expression:

[tex]$$
\frac{500}{800000}.
$$[/tex]

Step 4. Simplify the fraction

Dividing [tex]$500$[/tex] by [tex]$800000$[/tex] gives:

[tex]$$
\frac{500}{800000} = 0.000625.
$$[/tex]

Step 5. Express the result in scientific notation

To convert [tex]$0.000625$[/tex] to scientific notation:

[tex]$$
0.000625 = 6.25 \times 10^{-4}.
$$[/tex]

Thus, the expression is equivalent to

[tex]$$
6.25 \times 10^{-4}.
$$[/tex]

Final Answer: Option A is correct.

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