If $ x $ and $ y $ have $ n $ significant places, how many significant places do $ x + y $, $ x - y $, $ x \times y $, $ x / y $, $ \sqrt{x} $ have?
I want to evaluate expressions like $ \frac{ \sqrt{ \left( a - b \right) + c } - \sqrt{ c } }{ a - b } $ to $ n $ significant places, where $ a $, $ b $, $ c $ are nonnegative integers. I was thinking about doing it recursively, i.e., if want to evaluate $ x / y $ to $ n $ places, I need to evaluate $ x $, $ y $ to $ m $ places, if want to evaluate $ x - y $ to $ n $ places, I need to evaluate $ x $, $ y $ to $ m $ places...
What book should I be reading?