+1833 1. Convert 35 from base 10 to base 2. (You do not need to include the subscript 2 in this answer.)
2. The decimal number 61 is a 2-digit number. Find the smallest positive integer $B$ so that when we express the decimal number 61 as a base $B$ number we still get a 2-digit number.
+128579 a) 352 =1*(2)^5 + 0*(2)^4 + 0*(2)^3 + 0* (2)^2 +1*(2)^1 +1*(2)^0 = 100011 in base 2
b) Notice that, in base 7, 6*(7)^1 + 6*(7)^0 = 42 + 6 = 48.... and this is too small
However, in base 8, 7(8) .... 7*(8)^1 + 5*(8)^0 = 56 + 5 = 61 ......so 8 is the smallest possible base that will still produce a two digit number equal to 61 ......the notation is 758
+1833 Sorry everybody for all of the questions!!! I missed you all!! I haven't been on here for a while :)
+128579 a) 352 =1*(2)^5 + 0*(2)^4 + 0*(2)^3 + 0* (2)^2 +1*(2)^1 +1*(2)^0 = 100011 in base 2
b) Notice that, in base 7, 6*(7)^1 + 6*(7)^0 = 42 + 6 = 48.... and this is too small
However, in base 8, 7(8) .... 7*(8)^1 + 5*(8)^0 = 56 + 5 = 61 ......so 8 is the smallest possible base that will still produce a two digit number equal to 61 ......the notation is 758
