Not true when cutting an already butchered steak into small pieces for something like fajitas.
Or at least if it was not done against the grain you can cut your small pieces off in a way that is against the grain
All the round steaks I have ever seen in the supermarket have already been butchered across the grain so it's likely that OP's steak was done that way as well. This includes round roasts. Skirt steaks are different and go with the grain typically due to their arrangement on the carcass so it is possible to cut across the grain after butchering, but I've never seem a top round steak that went with the grain, with the exception of eye of round which is intentionally butchered with the grain. If OP had and eye of round for dinner, then he would likely have cut off slices across the grain already so I still don't think it applies here.
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