$(10$ pts$)$ Consider two positive nearly equal numbers $$ and $,$ where $$ is given with $6$ significant digits

and $$ with $4$ significant digits. Answer the following questions:

a$)$ Calculate the maximum possible value of the error for the sum of these two numbers? Hint: Think

of absolute error in $$ and $$ in terms of stopping criteria used for terminating iterative algorithms.

b$)$ Givenapproximatevaluesof$3\mathrm{.}25417$and$3\mathrm{.}252,$findtheapproximatevalueof

$=.$ What is the maximum possible value of the relative error in $?$ Compare this error to the maximum possible value of the relative error for numbers $$ and $.$