Which statement is correct?

A. [tex]\(\frac{3.56 \times 10^2}{1.09 \times 10^4} \leq \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right)\)[/tex]

B. [tex]\(\frac{3.56 \times 10^2}{1.09 \times 10^4} \ \textless \ \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right)\)[/tex]

C. [tex]\(\frac{3.56 \times 10^2}{1.09 \times 10^4} \ \textgreater \ \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right)\)[/tex]

D. [tex]\(\frac{3.56 \times 10^2}{1.09 \times 10^4} = \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right)\)[/tex]



Answer :

Let's carefully examine and compare the two expressions given in the question:

1. Evaluate the first expression: [tex]\(\frac{3.56 \times 10^2}{1.09 \times 10^4}\)[/tex].

2. Evaluate the second expression: [tex]\(\left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right)\)[/tex].

First, we will simplify each expression individually.

1. First Expression:
[tex]\[ \frac{3.56 \times 10^2}{1.09 \times 10^4} \][/tex]
We know from our calculations that this simplifies to:
[tex]\[ 0.0326605504587156 \][/tex]

2. Second Expression:
[tex]\[ (4.08 \times 10^2) \times (1.95 \times 10^{-6}) \][/tex]
We know from our calculations that this simplifies to:
[tex]\[ 0.0007956 \][/tex]

Now, let's compare the two values:

- We have:
[tex]\[ 0.0326605504587156 \][/tex]
and
[tex]\[ 0.0007956 \][/tex]

It is evident that:
[tex]\[ 0.0326605504587156 > 0.0007956 \][/tex]

Thus, the correct statement is:
[tex]\[ \frac{3.56 \times 10^2}{1.09 \times 10^4} > \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right) \][/tex]

Therefore, the correct statement is the third one:
[tex]\[ \frac{3.56 \times 10^2}{1.09 \times 10^4} > \left(4.08 \times 10^2\right) \left(1.95 \times 10^{-6}\right) \][/tex]