Every block will have a vote in it. A value between 0-100.

Obviously whoever finds the block gets to write in that value.
Much like he gets to write in his coinbase tx.

So every block has a vote. Those blocks that don't have a vote (because they are from the previous version) are considered a zero vote.
(this will only have to be considered during the 24 hour interim period after we do the fork. After that it is mandatory protocol for a miner to fill in the vote value.)

How do we now calculate the percentage that goes to the servicenodes?

By looking at the last 1440 blocks, by reading all those 1440 votes and calculating the average of all those votes.

With every new block we repeat this.
Again we look at the last 1440 blocks, which are now 1 block higher, so the average will be slightly different.

And we just repeat this over and over. There is no "voting period" as you say, it just happens continuously, much like new blocks do appear on a constant more or less predictable basis.
(average once a minute).

In effect we are looking at all the votes of the last 24 hours.

And as the globe spins, we are spinning with it!  

BTW: With an average over 1440 values we will see a very steady smooth curve.
The maximum the percentage can be moved from one block to the other is 0.07% (that's in the absolute outlier case of having 1439 "0" votes, and 1 "100" vote.)