To determine which numbers are less than [tex]\( 8.1 \times 10^{-8} \)[/tex], we need to compare each given number with the threshold value [tex]\( 8.1 \times 10^{-8} \)[/tex].
1. Compare [tex]\( 8.2 \times 10^{-8} \)[/tex] with [tex]\( 8.1 \times 10^{-8} \)[/tex]:
[tex]\[ 8.2 \times 10^{-8} > 8.1 \times 10^{-8} \][/tex]
Thus, [tex]\( 8.2 \times 10^{-8} \)[/tex] is not less than [tex]\( 8.1 \times 10^{-8} \)[/tex].
2. Compare [tex]\( 7.3 \times 10^{-5} \)[/tex] with [tex]\( 8.1 \times 10^{-8} \)[/tex]:
Since [tex]\( 10^{-5} \)[/tex] is a larger exponent than [tex]\( 10^{-8} \)[/tex], we can easily see that:
[tex]\[ 7.3 \times 10^{-5} > 8.1 \times 10^{-8} \][/tex]
Thus, [tex]\( 7.3 \times 10^{-5} \)[/tex] is not less than [tex]\( 8.1 \times 10^{-8} \)[/tex].
3. Compare [tex]\( 9.2 \times 10^{-9} \)[/tex] with [tex]\( 8.1 \times 10^{-8} \)[/tex]:
Since [tex]\( 10^{-9} \)[/tex] is a smaller exponent than [tex]\( 10^{-8} \)[/tex], we know that:
[tex]\[ 9.2 \times 10^{-9} < 8.1 \times 10^{-8} \][/tex]
Thus, [tex]\( 9.2 \times 10^{-9} \)[/tex] is less than [tex]\( 8.1 \times 10^{-8} \)[/tex].
4. Compare [tex]\( 3.4 \times 10^{-10} \)[/tex] with [tex]\( 8.1 \times 10^{-8} \)[/tex]:
Since [tex]\( 10^{-10} \)[/tex] is a smaller exponent than [tex]\( 10^{-8} \)[/tex], we know that:
[tex]\[ 3.4 \times 10^{-10} < 8.1 \times 10^{-8} \][/tex]
Thus, [tex]\( 3.4 \times 10^{-10} \)[/tex] is less than [tex]\( 8.1 \times 10^{-8} \)[/tex].
Therefore, the numbers that are less than [tex]\( 8.1 \times 10^{-8} \)[/tex] are:
[tex]\[ 9.2 \times 10^{-9} \text{ and } 3.4 \times 10^{-10} \][/tex]
So, the correct answers are:
[tex]\[ 9.2 \times 10^{-9} \][/tex]
[tex]\[ 3.4 \times 10^{-10} \][/tex]
