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What is the sum of all the digits of the integers between 1 to 2008?
The sum of all the the integers between 1 and 2008 (2 through 2,007) is 2,017,036.
The last two digits of 5347?
are the last TWO digits of 5347. 5, 3, 4, and 7 are all digits of the number 5347.
Can all of the digits of pi be fully known?
No, they cannot. Even the concept of "all the digits of pi" is a problem. On the bright side, you don't have to get too many digits in before you have more than enough accuracy for any application you can imagine. Pi may be irrational, but it is reasonable nonetheless. The only digits I memorized to is 3.14159265358979323846264338327950288419716939937510.....that's all a 6th grade math book can give ya. The number being irrational means that it will go on and on forever. So, because of this is it not possible to know all the digits, because there will always be more to know.
Is the subset H of 0 1 consisting of all decimals that are 100 digits long infinite or finite?
It's finite (although very big). If a decimal between 0 and 1 is exactly 100 digits long, then there are 10 ways to choose the first digit, 10 ways to choose the second, and so on. This gives us 10100 ways to choose all 100 digits, which is very large (it's a googol, in fact) but not infinite.
How many 3 digit numbers can be formed using the digits 2 3 5 6 7 9 if repetition of digits is not allowed?
120 There are 6 digits in total. The numbers with 3 digits, with all digits distinct from each other, are the permutations of the 6 digits taken 3 at a time, and therefore there are 6*5*4 = 120 of them.
