Option B: [tex]$4.5 \times 10^{-6}>3.9 \times 10^{-9}$[/tex] is the correct answer.
Explanation:
Option A: [tex]$7.1 \times 10^{8}>1.2 \times 10^{9}$[/tex]
Simplifying, we get,
[tex]710000000>1200000000[/tex]
Since, the value of [tex]$1.2 \times 10^{9}$[/tex] is greater than [tex]$7.1 \times 10^{8}$[/tex], the comparison [tex]$7.1 \times 10^{8}>1.2 \times 10^{9}$[/tex] is false.
Hence, Option A is not the correct answer.
Option B: [tex]$4.5 \times 10^{-6}>3.9 \times 10^{-9}$[/tex]
Simplifying, we get,
[tex]0.0000045>0.0000000039[/tex]
Since, the value of [tex]$4.5 \times 10^{-6}$[/tex] is greater than [tex]$3.9 \times 10^{-9}$[/tex], the comparison [tex]$4.5 \times 10^{-6}>3.9 \times 10^{-9}$[/tex] is true.
Hence, Option B is the correct answer.
Option C: [tex]$2.4 \times 10^{-5}<5.7 \times 10^{-6}$[/tex]
Simplifying, we get,
[tex]0.000024<0.0000057[/tex]
Since, the value of [tex]$2.4 \times 10^{-5}$[/tex] is greater than [tex]$5.7 \times 10^{-6}$[/tex], the comparison [tex]$2.4 \times 10^{-5}<5.7 \times 10^{-6}$[/tex] is false.
Hence, Option C is not the correct answer.
Option D: [tex]$8.2 \times 10^{-4}<3.6 \times 10^{-6}$[/tex]
Simplifying, we get,
[tex]0.00082<0.000036[/tex]
Since, the value of [tex]$8.2 \times 10^{-4}$[/tex] is greater than [tex]$3.6 \times 10^{-6}$[/tex], the comparison [tex]$8.2 \times 10^{-4}<3.6 \times 10^{-6}$[/tex] is false.
Hence, Option D is not the correct answer.
