Unfortunately, the BLS monthly job numbers' margin of error is never "disclosed" when the numbers are reported or shown on the news networks. Go ahead and see if you can find it or hear it mentioned today when the number is reported by all the news networks - I bet you can't. Now why do you suppose that is?
You won't ever see it disclosed because the dirty little secret is hidden in the BLS report under "The Employment Situation Technical Note." Just scroll down the page and find the heading "Reliability of the estimates" and start reading. There you will find some information that may be just as important as the actual monthly job's number itself. Did you find it yet? Are you shocked by the "margin of error" number?
That's right, the BLS margin of error for monthly job numbers is: +/- 100,000.