a 10.0 kg mass has a potential ebergy of 10.0 j when it is at what height
I think
PE = m*g*h
10 = 10*9.8*h
h = 1/9.8
$${\frac{{\mathtt{1}}}{{\mathtt{9.8}}}} = {\frac{{\mathtt{5}}}{{\mathtt{49}}}} = {\mathtt{0.102\: \!040\: \!816\: \!326\: \!530\: \!6}}$$
I think that is 0.102 metres.
(on Earth, at sea level)