Question
Which statement is correct?
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) less-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than-or-equal-to StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) = StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) less-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than-or-equal-to StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) = StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
Answers
GPT-4o mini
To determine which statement is correct, we need to calculate both sides of the inequality and see where they stand relative to each other.
First, let's compute the left-hand side:
\[
(2.06 \times 10^{-2}) \times (1.88 \times 10^{-1}) = 2.06 \times 1.88 \times 10^{-2} \times 10^{-1} = 3.8688 \times 10^{-3}
\]
Next, we'll compute the right-hand side:
\[
\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}} = 7.69 \div 2.3 \times 10^{-2 - (-5)} = 3.34347826087 \times 10^{3} \approx 3.34 \times 10^{3}
\]
Now we can compare both results:
- The left-hand side is approximately \(3.8688 \times 10^{-3}\).
- The right-hand side is approximately \(3.34 \times 10^{3}\).
Since \(3.8688 \times 10^{-3}\) (which is a very small number) is much less than \(3.34 \times 10^{3}\) (which is a much larger number), we can conclude:
\[
(2.06 \times 10^{-2}) (1.88 \times 10^{-1}) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\]
Thus, the correct statement is:
\[
(2.06 \times 10^{-2}) (1.88 \times 10^{-1}) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\]
First, let's compute the left-hand side:
\[
(2.06 \times 10^{-2}) \times (1.88 \times 10^{-1}) = 2.06 \times 1.88 \times 10^{-2} \times 10^{-1} = 3.8688 \times 10^{-3}
\]
Next, we'll compute the right-hand side:
\[
\frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}} = 7.69 \div 2.3 \times 10^{-2 - (-5)} = 3.34347826087 \times 10^{3} \approx 3.34 \times 10^{3}
\]
Now we can compare both results:
- The left-hand side is approximately \(3.8688 \times 10^{-3}\).
- The right-hand side is approximately \(3.34 \times 10^{3}\).
Since \(3.8688 \times 10^{-3}\) (which is a very small number) is much less than \(3.34 \times 10^{3}\) (which is a much larger number), we can conclude:
\[
(2.06 \times 10^{-2}) (1.88 \times 10^{-1}) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\]
Thus, the correct statement is:
\[
(2.06 \times 10^{-2}) (1.88 \times 10^{-1}) < \frac{7.69 \times 10^{-2}}{2.3 \times 10^{-5}}
\]