Significant figures and normal distribution probabilities?

What is the connection between the number of significant figures in a z-value and the number of significant digits in the probability you get from a normal table or computer calculation?

For example, if you have heights from a population with µ = 63.5 and σ=2.80, and you want to find the probability that a randomly selected person has a height of less than 70.0 inches (so, we are working in decimal inches). You get z = (X-µ)/σ = (70.0-63.5)/2.80 = 2.32142857143.

If you are using a table, you are forced to either:

(1) look up 2.32 in a table to get a probability of 0.98983​
(2) interpolate using the table, which I am not going to bother doing because the answer wouldn't be as accurate as . . .​
(3) use a computer command in some stat software to get an answer like pnorm(2.32142857143) = 0.9898681.​

Here's the question: If I am being careful about significant digits, should I report my final answer as 0.990 (three significant digits) because that's how many the z-value I was looking up had (I didn't round the 2.32142857143 because we aren't supposed to round intermediate calculations.)? Or is there some other relationship between z-values and probabilities when it comes to significant figures?
Follow-up question: If your z-value is 0.08 or 0.080 or 0.0800, how many significant figures do you have from the number you look up in the table? Or does it not matter because you don't round until the end and you will round to however many significant figures you had in the number with the smallest number of significant figures?