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I doubt banks would take 52% notes... So if it's "around" 50%, both pieces are probably worthless.

And writing this it occurred to me: the way to tear it well is the way you do with a piece of paper: fold it in half aligning the corners, make a good crease, and tear slowly...

In the US paper currency has two copies of a serial number printed on the right half and left half of the face. both copies of the serial numbers must be present for the note to have any value.

There is more specific information at the bottom of this page [0], linked from your one. There are a couple of provisions, but most relevant is that you need "clearly more than 50 percent" of the note in a case like this.

[0] https://www.bep.gov/services/currencyredemption.html