I was shopping at BHG at Century Square just now.... got a few
ten-dollar notes as change for some stuff I bought. I just flipped
through the notes to make sure my change was correct and stuffed
the whole lot down my pocket since I was in a hurry....
Then much later on, when I was at Parkway Parade, I took the
notes out of my pocket....
Guess what.... one of the ten-dollar notes was cleanly cut right
down the middle. 
It wasn't a tear because the edges were clean and not jagged.
Hell, it was one of the new polymer notes which are difficult to
tear (accidentally or not).
If I wasn't so busy, or so far away from Tampines, or the note
had been bigger, I'd have marched back to the store there and
created a huge ruckus....
It's still legal tender (no matter what the cashier you give it
to in the future says) and you can tape it back together.