Engineers are not mathematicians. Neither are scientists. On a macro scale there may be a very significant difference, there may not be. That’s why science developed the policy of significant figures. (ie, if you start with two decimal places, you end with two decimal places rounded up or down as needed.)
Math is different. Pure math has the consensus, the general rule, that answers are significantly accurate at six decimal places. This stems from Newton’s assertations when he was developing his theories and laws. Thus, the square root of 3 is accurately described as 1.732051 with the last 808 rounded up.
Now, if your specific engineering instance demands a higher degree of certainty, that does not mean that the mathematical accuracy is wrong, it means you, personally, need more accuracy. No one is stipulating that 1.732050808 is less accurate or of the same accuracy. Mathematicians just stipulate that, for the purposes of pure math, 1.732051 is accurate enough, or 6 decimal places are the limit of significance we need to continue on to the next step of the problem.
Trust me, just leave the mathematical theory to the mathemeticians and stick to doing your own job. Build something with the formulas, laws and theorems we give you.