Your question itself is obscure. You don’t say what it was that you were calculating, or why, or the measurement uncertainty of whatever quantity or units you were discussing.
Given your example, you said that your answer “had several numbers [sic, “digits”, not numbers. We’re assuming the calculated value is “a number”, and the number is composed of digits.] after the decimal point”. Well, fine. But could anyone measure to those thousandths or ten-thousandths? If you’re talking, for example, about how much of an apple each of three people could eat if they shared it equally and your response is that “Each person could eat 0.33333333333 [and so on] of an apple,” then the response is technically correct – and ludicrous. Because no one can measure and compare one quantity of apple to another to so many decimal places; it’s not even scientifically realistic. It just can’t be done.
So responses on most kinds of consumer-type issues (or “kitchen science”, if you prefer) can be accurate beyond one’s ability to measure to that level of precision. In the above example, then, saying that “each person could eat a third of an apple” is also technically precise – the same level of scientific and literary precision, anyway – but it allows for the fact that no one in a normal kitchen can estimate much better than ⅓ apple ± about ½ of the ⅓.
Extending a calculated response to the thousandth’s place implies 1) that you can measure to that level of precision and 2) that it matters. It doesn’t usually, or even very often.
On the other hand, if you can estimate (or recall) π to multiple levels of precision, then have at it. Especially when you’re figuring orbital mechanics, where it might actually matter.