How do you determine whether to use 22/7 or 3.14 for π?

Use the value the problem statement tells you. Otherwise, use a better approximation.

Step-by-step explanation:

π ≈ 3.141592653589793238 ... (a non-repeating infinite decimal)

3.14 = 3.14

22/7 = 3.142857142857_142857

355/113 = 3.14159292035 ... (a very long repeating decimal)

You can see that the third decimal place is wrong in both of your approximations. The last approximation shown has 7 good decimal digits. A good scientific or graphing calculator will have an internal value for pi that is good to 10 or 12 digits or more (preferably, at least 32 digits).

You should use a value for pi that has at least one more digit of accuracy than the number of significant digits in your answer.