#### Answer

The student's answer was not the EXACT answer since it is rational.

#### Work Step by Step

$\sin$ 45$^{\circ}$ = $\frac{1}{\sqrt2}$
$\frac{1}{\sqrt2}$ is irrational. Meaning that it does not have a finite set of digits.
0.7071067812 is rational. This means that the student's answer was not the EXACT answer since it is rational.