How do ballet dancers stay so thin?

Professional dancers probably eat more than the average person. But yes, they burn so many calories it keeps them thin. 

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There is also what's known as the "ballet body". Ballet works particular muscles in particular ways that tend not to "bulk you up" and give a very lean, toned appearance. So if this is a person's main source of exercise, even if they aren't dancing professionally, they might be more likely to look thin in comparison to a soccer player or something. 

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There is also the unfortunate fact that ballet prefers naturally thin bodies. Girls who are naturally thin, have naturally broad shoulders, naturally toned, naturally flat-chested, naturally flexible bodies are preferred in dance. They receive a lot more encouragement from teachers at a young age because they are naturally built for ballet. They are often said to have more "potential". So it's also probably true that lots of ballet dancers just happen to be naturally thin people. 

They dance the calories away!

We burn most of calories when we dance

If you were taking ballet/dance classes for 4-8 hours a week, that physical activity would help. They eat healthy. 

Not all are thin, not all are eating healthy. 

My daughter grazes through out the day instead of eating three big meals.  She never has pop/soda. She drinks mainly water. 

Staying healthy and at a good weight requires exercise and eating right. 

Dancing makes then lose weight.. See dancing 8+hrs a day is so much.so ofcourse they'll lose weight cuz of dancing

dancing might make them lose weight

Technically, if You've been doing exercise for a long period of time, even if it's infrequent or weekly, You are still bound to see change. It can also depend on metabolism as well.