The clearing standard is $0.01 in the money. Individual brokers often apply stricter rules, declining to exercise where the client lacks the cash, or exercising anything with intrinsic value regardless of size.
The lesson is to know your broker's policy rather than the industry default, and to close cheap long options rather than let expiration decide. Selling a $0.02 option for $2 is better than being handed a stock position worth $5,000.
Example: XYZ closes at $50.005. Under a one-cent rule the $50 call is not exercised. At $50.01 it is. Half a cent decides whether you wake up flat or long 100 shares — which is why traders flatten near-the-money longs before the close rather than testing the rule.
Related: exercise-by-exception, occ, pin-risk, expiration-date