# 999

1. ### Smallest multiple of 999

which is the smallest multiple of 999 which does not contain the number 9 ? I need to know how to solve this one, not brute force.
2. ### decimal expansion of 7^999,999

I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem. Find the decimal expansion of {7}^{999999}. Thanks for the help.
3. ### Find the remainder in the range 0 to 999 when 7^(8^9) is divided by 1000

Hey guys, Im confused with this :s Find the remainder in the range 0 to 999 when 7^(8^9) is divided by 1000 We're dealing with a huge power, and it confused me as to how I am supposed to work it out. I could start with doing 7 = 7 mod 1000 7^2 = 49 mod 1000 7^3 = 343 mod 1000...
4. ### How many five digit integers (10,000-99,999) are divisible by 5?

When I did it I got 2000*10-2000=18000. But I was marked wrong but cant see where I went wrong.
5. ### proof that the proof that .999_ = 1 is not a proof (version)

hello! i think this should be posted here because, theoretically, this part of the forums is for the practical people, and they are the people most likely to appreciate this post. please respond and let me know what you think - but try not to tell me anything that i already know (e.g...
6. ### .999... = 1?

I have heard that .999 with a repeating 9 equals exactly 1. Can someone please discuss this here? Why is it true?