Zero's Special Rules

Adding zero changes nothing: a + 0 = a. Multiplying by zero wipes everything out: a × 0 = 0. Dividing by zero is undefined — not infinity, not zero, just meaningless. Your calculator flashes "Error" because no number, times zero, can ever give you back anything but zero.

Some decimals stop neatly (0.25, 0.125) while others run forever (0.333..., 0.142857...). The deciding factor is the bottom number's prime factors. In base 10, only 2s and 5s can produce a decimal that terminates. Any other factor lurking in the denominator forces the digits to repeat without end.