Final answer:
The value 2.32192809 rounded to the nearest hundredth is 2.33 because the digit in the thousandths place is an 8, which is greater than 5, necessitating a round up of the hundredths place to 3.
Step-by-step explanation:
The value x=2.32192809 rounded to the nearest hundredth is 2.33. To round a number to the nearest hundredth, you look at the third decimal place, which is the thousandths place in this case. If this digit is 5 or greater, you round the second decimal place (hundredths place) up. If it is 4 or less, you leave the second decimal place as it is. Since the third decimal place in 2.32192809 is an 8, which is greater than 5, we round the second decimal place up from 2 to 3. Hence, the rounded value would be 2.33, making option B the correct answer.