Listen to the audio. (3:10)
We have a very brief Davar Halacha today before we begin Slichot.
The question is: As it is a fast day, what should you do if you make a mistake and eat, or perhaps if you made a mistake and ate already? In my experience this is one of the most commonly misunderstood Halachot regarding fast days.
The Mishnah Brurah (549:3) says (Listen to audio for the Hebrew):
One who erred, one who made a mistake and ate on one of the public fast days, in spite of the fact that he has already eaten, he has to continue the fast and complete it — even after he already ate. Just because he ate already, so he should continue eating through the public fast day!? And perhaps he should fast another day to make it up? Look in Simon 568...
... and we'll go over there and look at what is says... in Simon 568, the Mechaber writes:
One who makes a neder (vow) to fast on a particular day, and forgets his neder and he eats, he should complete his fast nonetheless. (That is to say that after he ate, he should complete his fast on the rest of the day.) The din and the halacha are the same, if it was a fast for a dream (there is a halacha regarding fasting if you have had a bad dream) or a public fast day.
One who forgets should continue to fast.
The Mishnah Brurah writes:
Even one who purposely broke the fast and ate a lot, should nonetheless stop eating and continue the fast.
In other words, you purposely broke the fast and ate, nonetheless says the Mishnah Brurah, you should do Teshuva and part of the Teshuva is finishing the fast.
With regard to being "mashlim the ta'anit", explains the Mishnah Brurah, you are required not only to finish that fast day, but to make up the fast on another day, that is, to do Teshuva by fasting on another day for having eaten on a fast day.
As I said in the begining, in my experience, this is one of the most commonly understood Halachot. It seems that people have the thought that if you accidentily ate, so that's it — your fast is over. In fact, we see it very clearly from the Mishnah Brurah and the Shulchan Aruch that it is not the case.