Wikipedia: When Demetrius of Phalerum conducted a population census [of Athens] in 317 BC the population was 21,000 free citizens, plus 10,000 resident aliens and 400,000 slaves.
How do you prevent an uprising with those numbers?
Centuries of internalized repression.
Probably not; the ancient Greeks generally didn't allow their slaves to have children of their own, so few were born into slavery.
Maybe a slave's life in that society was not as bad as you think.
Many greek slaves had decent enough lives, especially if they were educated, they might be running their masters business and have quite a lot to lose in a rebellion and not much of an upside. Greek slavery was not at all like the antebellum South.