To determine which statement is correct, we need to evaluate both sides of each inequality or equality, step-by-step.
First, let's evaluate the left side:
[tex]\[
\left(2.06 \times 10^{-2}\right) \times \left(1.88 \times 10^{-1}\right)
\][/tex]
Multiplying the constants:
[tex]\[
2.06 \times 1.88 = 3.8728
\][/tex]
Next, we combine the exponents of 10:
[tex]\[
10^{-2} \times 10^{-1} = 10^{-3}
\][/tex]
Therefore:
[tex]\[
\left(2.06 \times 10^{-2}\right) \times \left(1.88 \times 10^{-1}\right) = 3.8728 \times 10^{-3} = 0.0038728
\][/tex]
Next, let's evaluate the right side:
[tex]\[
\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\][/tex]
We first divide the constants:
[tex]\[
\frac{7.69}{2.3} = 3.344782608695652
\][/tex]
Next, we divide the powers of 10:
[tex]\[
10^{-2} / 10^{-5} = 10^{-2 - (-5)} = 10^{3}
\][/tex]
Therefore:
[tex]\[
\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}} = 3.344782608695652 \times 10^{3} = 3343.4782608695655
\][/tex]
Now, we compare the left side and the right side:
[tex]\[
0.0038728 \quad \text{and} \quad 3343.4782608695655
\][/tex]
Clearly:
[tex]\[
0.0038728 < 3343.4782608695655
\][/tex]
Thus:
[tex]\[
\left(2.06 \times 10^{-2}\right)\left(1.88 \times 10^{-1}\right) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\][/tex]
The correct statement is:
[tex]\[
\left(2.06 \times 10^{-2}\right)\left(1.88 \times 10^{-1}\right) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\][/tex]
So, the first statement is correct.
