# Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,Times et cetera preserve precision digits?

• Does that include things like Sin, Exp, and other mathematical expressions? – Sjoerd C. de Vries Dec 24 '14 at 12:09
• @SjoerdC.deVries Yes, Exp, ^, /, etc. The most usual ones – An old man in the sea. Dec 24 '14 at 12:33
• It depends on the magnitude of the numbers and what you mean by "preserve". For example, adding 1.600 to 10.600^601 obviously loses all of the 600 digits of precision of the 1. – Oleksandr R. Dec 24 '14 at 13:51
• I would say the answer is yes to what I would guess is your question: All the mathematical functions keep track of precision given arbitrary-precision numbers for input. "Preserve" is a confusing term, since in subtracting like-sized numbers, you lose a significant amount of precision, according to how precision is supposed to be calculated (which is what happens in Mathematica). – Michael E2 Jan 26 '15 at 14:41