What did I do wrong in my temperature change calculations?
You're not really wrong: the computer program is apparently expecting a float and not an integer, which is really stupid because the question is about temperature change and not the vagaries of significant figures.
Instead of you learning about heat capacity and the relation to temperature change, you're instead learning about significant figures first, and the chemistry/physics part second.
I find this sort of thing patently awful and a frustrating way for you or anyone else to &quot;learn&quot; anything about the principles.
You have to report your answer to 2 significant figures:
750 has 2 (the limiting number); 31500 has 3; and 4.184 has 4.
$$Q = m\times c\times \Delta T$$
or
$$\Delta T = {Q\over m\times c}$$
so
$$\Delta T = {31,500\ {\rm J}\over 750\ {\rm g} \times 4.184\ {\rm J}\cdot {\rm g}^{-1}\cdot {\rm ^{\circ}C}^{-1}}$$
which, to 2 significant figures, is:
$$\Delta T = 10.\ ^{\circ}{\rm C}$$
Notice I have included a decimal point, so the now ridiculous answer that should be accepted is 10. and not 10
Meanwhile, you've lost a lot of time wondering where your calculation went wrong because some programmer doesn't know how to cast. Or maybe you're really supposed to report numbers with a terminal decimal point, and I'll challenge anyone to find any respected publication where that happens:

&quot;The temperature change, in degrees Celsius, is 10..&quot;

Note that 10.0 has three significant figures, so that's also &quot;wrong.&quot;
And that, my friend, is why &quot;learning&quot; from a computer is a lazy way out for the &quot;teacher.&quot;