To round the number [tex]\(2.140959222634\)[/tex] to the nearest nine decimal places, follow these steps:
1. Identify the digit at the ninth decimal place: In the given number [tex]\(2.140959222634\)[/tex], the digit at the ninth decimal place is '2'. We will underline the digit we want to round to:
[tex]\(2.140959222\underline{6}34\)[/tex]
2. Look at the digit immediately following the ninth decimal place: The digit following '2' is '6', which is at the tenth decimal place.
3. Determine whether to round up or down:
- If this next digit is 5 or greater, we round up.
- If this next digit is less than 5, we keep the digit at the ninth decimal place as it is.
In this case, the digit following '2' is '6', which is greater than 5, so we need to round up.
4. Apply rounding:
- Given that the digit in the tenth place (6) is greater than 5, we add 1 to the ninth decimal place digit (2).
Rounding [tex]\(2.140959222\underline{6}34\)[/tex] results in:
[tex]\(2.140959223\)[/tex]
Thus, the correct answer is [tex]\( \text{B. } 2.140959223 \)[/tex].
