implicit-hydrogen convention

If skeletal drawings showed every hydrogen, a molecule like cholesterol would be a thicket of fifty-odd H's and you would lose the structure in the clutter. The implicit-hydrogen convention is the agreement that lets chemists leave the hydrogens off carbon and just trust the reader to fill them back in mentally. It works because carbon almost always wants exactly four bonds.

Here is the rule that makes it watertight. Carbon forms four bonds. Look at any carbon in a skeletal drawing, count the bonds you can see going to other drawn atoms, and the number of hydrogens on that carbon is four minus that count. A line-end carbon shows one bond, so it has three hidden hydrogens (a CH3). A carbon at a simple vertex shows two bonds, so it has two hidden hydrogens (a CH2). A carbon at a double bond counts the double bond as two of its four bonds. Heteroatoms follow their own valences — oxygen wants two bonds, nitrogen three — and crucially their hydrogens are written out, because you cannot reliably guess them and because they often carry the chemistry (the acidic O-H, the basic N-H).

This convention is what makes skeletal structures readable, but it is also the number-one source of beginner errors. Forget that a line-end is CH3 and you will write the wrong molecular formula; miss that a carbon already has a charge or a lone pair and you will add too many hydrogens. The cure is mechanical: at every carbon, the visible bonds plus the implicit hydrogens must add up to four.