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1. Literally, to cross something or some place either by literally running or by travelling very quickly. She ran across the street to tell me the news. I have to run across town to deposit some money into my bank account.
2. To find or see someone or something incidentally. I ran across him in the library after work, and we got into a great conversation about Hemingway. I ran across a $20 bill on my way to school this morning! If you run across my jacket, please let me know. I forget where I left it.
run across something
to cross something while running. The joggers all ran across the bridge together. The mice ran across the floor, not knowing that a cat was watching them.
To find someone or something by chance; come upon someone or something: I ran across some old friends at the store.