How do you drop the last part of a number, which is of less importance?

If the topic of your conversation has to do with natural sciences, you could use the scientific notation to give approximations with arbitrary precision.

In your examples, you would say "one point two", "two point one thousand", "one point three million" etc.

It will be generally understood that "one point three million" refers to a number greater than "one point two million" but lesser than "one point four million".

If you're not speaking or writing formally, you can use "odd".

He's sixty-odd years old.
It cost fifty-odd thousand dollars.
He has two-thousand-odd chickens on his farm.
A million-odd people live in San Jose.

I don't find it idiomatic for single-digit numbers like "one" or "two". So I wouldn't recommend saying:

*We waited two-odd hours.

(Although Google does find a few hits for "two-odd hours".)

I'm unclear of your question.

If you are asking "what phrasing can I use to indicate an approximate range", then consider:

• "I waited an hour or two."
• "I waited an hour and a half, give or take a half an hour."

If you are asking "how do I instruct/request someone to be less specific", you can consider:

• "Let me know the expected wait time, rounded to the nearest half hour."
• "Please give me an estimate of the shortest and longest likely wait time."
• "About how long will I have to wait?" -- then do the rounding yourself!

The scientific concept you are getting at is one of precision. It seems in your wait time example, you want a duration with a precision of one hour (or half-hour, I'm not sure). In your numeric examples, you are seeking a precision of 1, one thousand, and one million, respectively. But outside of a technical situation, it would be awkward to request "please estimate the wait time with a precision of 30 minutes."