To find the value of [tex]\( e^{-\frac{1}{2}} \)[/tex] and round it to the nearest hundredth, we can follow these steps:
1. First, calculate the value of [tex]\( e^{-\frac{1}{2}} \)[/tex]. The number [tex]\( e \)[/tex] is a mathematical constant approximately equal to 2.71828. The expression [tex]\( e^{-\frac{1}{2}} \)[/tex] translates to [tex]\( e \)[/tex] raised to the power of [tex]\(-\frac{1}{2}\)[/tex].
2. Evaluating this, we obtain a value of approximately 0.6065306597126334.
3. Next, we round this value to the nearest hundredth. Looking at the third decimal place, which is 6, we see that it is greater than or equal to 5. Therefore, we round up the second decimal place.
After rounding, the value of [tex]\( e^{-\frac{1}{2}} \)[/tex] to the nearest hundredth is:
[tex]\[ \boxed{0.61} \][/tex]
Hence, out of the given choices, the correct answer is:
0.61
