what does the below math rebus puzzle mean?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

I’m tall when I’m young, and I’m short when I’m old. What am I?

There’s a one-story house in which everything is yellow. Yellow walls, yellow doors, yellow furniture. What colour are the stairs?

In the city of Brain Teasers, 5% of people do not list their phone numbers. Now if we select random 100 people from the phone directory, then how many people selected will have unlisted phone numbers?

It is raining today at 11:59 am. What is the probability of sunny weather after 72 hours?

In the four images below, can you find the odd one out?

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

Without looking at a calendar, within a minute name, a boy's name using 5 consecutive 1st letters of 5 consecutive months