Question

number has 6 digits smallest digit is 0.01 largest digit is 8,000 digit in the tens is 2 less than digit on the hundreds the sum of tens and hundreds is the digit in the thousands the digit in the tenths has the same value in every place the remaining digit is the largest even number

Answer 1

What a problem!  We know that the largest digit is 8,000, and the smallest is 0.01.  The number is 8,_ _ _._1.  If the tens is 2 less than the hundreds digit, then if we make the hundreds digit x, the tens are x-2.  The tens digit plus the hundreds digit is the thousands digit, so x+(x-2)=8.  Let's solve: x+(x-2)=8.  Eliminate parentheses: x+x-2=8.  Use inverse operations:x+x-2+2=8+2.  x+x=10.  Combine terms: x+x=2x.  2x=10.  Divide: 2x/2=10/2.  x=5.

So the hundreds digit, x, is 5.  And the tens are x-2: 5-2=3.  The number is 8,53_._1.  And what's the only number that means the same, no matter what place value you put it in?  0!  This is the tenths place: 8,53_.01.  The remaining digit is the ones.  The largest one-digit even number is 8, so our number is 8,538.01!

Answer: 8,538.01