Not sure if this question is right for this site, but I hope it will be okay. As an example, say I calculate a value of $\sim1.32755552$ that has three significant digits (say I divided two three-significant digit numbers together). How many insignificant digits (after the $1.32$) would I need to keep from this number if I wanted to multiply it with another number (say, with infinite significant digits) and get the same answer when rounded to the right number of significant digits as if I had a perfect measurement of a value?
Just to clarify, this comes up if you were to multiply $1.7$ (1 sig dig) by $3$ (infinite sig digs). If you didn't keep any insignificant digits, you would get $2\times3=6,$ but if you kept the $.7,$ you would get $1.7\times3=5.4,$ or $5$ when rounded one significant digit. Finally, the question is: How can one determine how many insignificant digits are needed to have an answer that is the same as a perfect measurement of the value, comparing up to the number of significant digits?
As this is a pretty sketchy question, if you need any clarifications on what I'm asking for, please leave a comment. I'll get back to you ASAP.