Let's evaluate each of the numbers given and determine which one is the greatest. The numbers provided are in scientific notation, and it helps to convert them to decimal form for clearer comparison.
1. Convert [tex]\(2.89 \times 10^{-8}\)[/tex] to decimal form:
[tex]\[
2.89 \times 10^{-8} = 0.0000000289
\][/tex]
2. Convert [tex]\(1.997 \times 10^2\)[/tex] to decimal form:
[tex]\[
1.997 \times 10^2 = 199.7
\][/tex]
3. Convert [tex]\(8.9 \times 10^{-6}\)[/tex] to decimal form:
[tex]\[
8.9 \times 10^{-6} = 0.0000089
\][/tex]
4. Convert [tex]\(5 \times 10^{-6}\)[/tex] to decimal form:
[tex]\[
5 \times 10^{-6} = 0.000005
\][/tex]
Now, we can directly compare the decimal values to find the greatest number:
- [tex]\(0.0000000289\)[/tex]
- [tex]\(199.7\)[/tex]
- [tex]\(0.0000089\)[/tex]
- [tex]\(0.000005\)[/tex]
From these comparisons, it's evident that [tex]\(199.7\)[/tex] is the largest value among the numbers.
Thus, the greatest number is:
[tex]\[ 1.997 \times 10^2 \][/tex]
