Learn English – Which is better, “customer number” or “customer count”

"The number of books is three" or "The quantity of water is three cubic meters" both sound rather convoluted and unnatural to me. Instead I'd suggest you say

There are three books

There are three cubic meters of water

Even when you are asked a question "What is the number of books?" it is much more common to respond "It is three" or "There are three books" or just "Three". There is no need to make a complicated answer!

I would recommend percentage, proportion, or fraction, depending on the exact usage required.

Your example can be reworded as

While the manufacturing sector's percentage of firms among public listings declined in the 1980's, its employment share increased significantly, which indicates a large rise in the average workers employed by a typical manufacturing firm in that period.

Side note: The conclusion you drew is not valid from the information presented. If the overall employment was shrinking and the manufacturing sector declined by some firms closing, while other sectors declined by laying off employees without many firms closing, then the total number of manufacturing employees could have dropped while the share of manufacturing employees rose. And in any case values for absolute numbers of employees by sector are likely readily available so there should be no need to try to infer this result indirectly.