81 / 2?

The early Tao was in two sections, the Tao (Way) Section (Chapters 1 to 37) and the Te (virtue/moral force) Section (Chapters 38 to 81) but it had very little formatting.   Within a few hundred years of the writing the first copy we know of,  the Tao had been formatted into 81 chapters.

3x3x3x3=81
3 is a really great Yang number because:

• Being an odd number, it has a left over, unpaired, unbalanced, unmatched unit.
• 3 in Chinese "san" sounds like the word for grow and give birth (sheng)
• The Chinese character for 3: , also looks like the character for birth:
• Three is mentioned in the Tao as the last stage of creation.

81 is the ultimate Yang number because it is 3x3x3x3.  This is probably why the Tao is in 81 chapters.

2 Sections
There are many theories about the rationale and chapter locations for the two  sections of the Tao.  Perhaps the importance of the splitting of the Tao is best explained in the last lines the first chapter:

Chapter 1
We desire to understand the world by giving names to the things we see, but these things are only the effects of something subtle.
When we see beyond the desire to use names, we can sense the nameless cause of these effects.
The cause and the effects are aspects of the same, one thing.
They are both mysterious and profound.
At their most mysterious and profound point lies the "Gate of the Great Truth".

Clearly here, the Tao and its physical manifestations are both important and worthy of separate explanation.