Use your work from Lab $3$ to complete this assignment, replacing the int data type with double and making the necessary adjustments.

Here is a tip on how to check for equality of double values in Java, along with an example:

Why We Can't Use $==$ Directly

The $==$ operator checks for exact equality. For floating$-$point numbers, due to precision issues, two values that should be equal might not be precisely the same. For example:

double a $=0\mathrm{.}1+0\mathrm{.}2$;

double b $=0\mathrm{.}3$;

if $($a $==$ b$)\{$

System.out.println$("$a and b are equal"$)$;

$\}$ else $\{$

System.out.println$("$a and b are not equal"$)$;

$\}$

Even though mathematically $01$ plus $02$ equals $030\mathrm{.}1+0\mathrm{.}2=0\mathrm{.}3,$ due to the way these values are stored in binary, a might not be exactly equal to b$.$

Correct Way to Check for Equality

To compare two double values, you should check if they are close enough to each other within a small tolerance $($epsilon$).$ This approach accounts for the possible precision errors.

double a $=0\mathrm{.}1+0\mathrm{.}2$;

double b $=0\mathrm{.}3$;

double epsilon $=1$e$-9$; $//$ Small tolerance value

if $($Math$.$abs$($a $-$ b$)<$ epsilon$)\{$

System.out.println$("$a and b are approximately equal"$)$;

$\}$ else $\{$

System.out.println$("$a and b are not equal"$)$;

$\}$

Explanation:

Calculate the Difference: Math.abs$($a $-$ b$)$ computes the absolute difference between the two values.

Compare with Tolerance: The difference is compared to a small value $($epsilon$).$ If the difference is smaller than epsilon, the values are considered equal.

Choose an Appropriate Epsilon: The choice of epsilon depends on the precision required by your application. Common values are $1$e$-6,1$e$-9,$ etc.