Is there a slang way to say numbers in Japanese, similar to how we say it in English?

Specifically -teen hundred.

Let's say my phone costs $1200. A lot of times, we don't say one thousand and two hundred dollars, we just say twelve hundred dollars. Obviously this isn't technically the correct way to say it, but it's just something we use to make saying long numbers faster. Is there something similar in Japanese?

Also, how do you actually say years? Let's say, 1965. In English we'd say nineteen sixty five. In Japanese would it be the same, so じゅういちろくじゅうご?