10 year old with two baby teeth that are rotting, how would dentists treat this?

Depends: If the teeth that are rotting are close to being replaced with permanent teeth, they he may do nothing. If they are causing infection, they will likely be pulled. Sometimes a spacer is used to hold the place for the permanent teeth, if it will be awhile before they come in. If they are not infected then they might be treated with crowns.

Extraction: From the age of the child , the permanent successor tooth is probably right under the rotted baby teeth, so best solution is to take them out is they are badly destroyed ..

Extract or leave : First make sure that the teeth are baby teeth, most ofthebaby teeth should be gone in another year or so. X rays should be taken to check the permanent teeth. If no infection then the rotten teeth can stay to keep the space , if not they should come out, otherwise they could cause damage to the permanent ones yet to come.

Several ways..: After proper radiographic exam, it will be clear what the condition of existing baby tooth is... Whether it needs baby root canal/pulpotomy, extraction, baby crowns, or even possibly removal . The main goal is to preserve the "space" for upcoming permanent tooth.

Infection: A rotting tooth is a badly infected tooth, and like any infection needs immediate attention. Infections can spread quickly. If tooth removal necessary ask your dentist about space maintenance and consultation w orthodontist. Infections don't cure themselves. Please get immediate help for your child.