The correct statement is that statement that correctly compares the expressions on both sides after both expressions have been simplified. The correct statement is: [tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) < 3.3435 \times 10^4[/tex]
Given that:
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1})[/tex] and [tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}}[/tex]
To determine the correct statement, we simply evaluate both expressions:
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1})[/tex] becomes
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 2.06 \times 10^{-2} \times 1.88 \times 10^{-1}[/tex]
Rewrite as:
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 2.06 \times 1.88 \times 10^{-2} \times 10^{-1}[/tex]
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 3.8728 \times 10^{-2} \times 10^{-1}[/tex]
Apply law of indices
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 3.8728 \times 10^{-2-1}[/tex]
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 3.8728 \times 10^{-3}[/tex]
Also:
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}}[/tex] becomes
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}} = \frac{7.69}{2.3} \times \frac{10^{-2}}{10^{-6}}[/tex]
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}} = 3.3435 \times \frac{10^{-2}}{10^{-6}}[/tex]
Apply law of indices
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}} = 3.3435 \times 10^{-2--6}[/tex]
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}} = 3.3435 \times 10^4[/tex]
At this point, we have:
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) = 3.8728 \times 10^{-3}[/tex] and
[tex]\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-6}} = 3.3435 \times 10^4[/tex]
By comparison:
[tex]3.8728 \times 10^{-3} <3.3435 \times 10^4[/tex]
Hence, the correct statement is:
[tex](2.06 \times 10^{-2})(1.88 \times 10^{-1}) < 3.3435 \times 10^4[/tex]
Read more about simplification at:
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