Ringworm is a fungus, and does not require the skin to be broken or scratched to pass from person to person, or animal to person, or even infected surface to person. It also isn't killed by normal soap and water, though, hand washing before and after every handling of each animal is always a good idea, because there are many things which can be washed off - namely fecal matter. Ringworm can be kind of a pain to get rid of, I've had to deal with it numerous times with various rescue animals. I'm not sure what treatment a vet would recommend for a number of rats, but it'd probably be worth a visit to have them all treated at once, at the same time as yourself, so you're not risking passing it back and forth while one or the other is being treated.

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The lips I never kissed, are lips I can't forget
The dress you never wore, on the day we never met
The name I never whispered, as it echoed in my mind
The man I never was, the sweet thing that's not mine.