Scientists often say that science is a cycle of "Experiment, fail, learn, repeat". Why is this an important concept in science and should this only apply in scientific research?

Because while doing research scientist follow the scientific metod.The scientific method involves exploration and observation and the search for the answer for a question. And there will always some hypotesis that while experimenting reveal to be wrong.

the density(ratio between mass and volume as m/v) decreases from top to bottom in periodic table group as the size increases and nuclear charge decreases. but in periods density increases from left to right as atom size decreases and nuclear charge increases.