finished bonus

Homework 11/bonus.tex

@@ -275,6 +275,14 @@ $11110000000000000.0 = 2^16 + 2^15 + 2^14 + 2^13 = 65536 + 32768 + 16384 +
 
 \section{Bonus Question 2}
 
+Loss of significance can occur via subtraction of values that are close to each other so
+that most of the significant digits get cancelled.
 
+For example let x $= 1.5 \times 2^0$
+and y $=\ 1.0 \times 2^{26}$ such that the sequence of operations $r =(x+y) - y $ results in r = 0.0 which is incorrect as the actual value should be 1.5.
+
+This is due to  catastrophic cancellation  which  occurred  during  the  subtraction.
+This kind of occurrences can't be identified unless data is further examined leaving no
+way of checking that 0.0 is the wrong result.
 
 \end{document}