



 
David, For a two digit number in base ten the leftmost digit is the tens digit and the rightmost digit is the units digit. Thus 43 is 4 tens and 3 units. For a two digit number in base b the leftmost digit is the b digit and the rightmost digit is the units digit. Thus 43_{b} is 4 bs and 3 units. So if b is 8 then 43_{8} is 4 eights and 3 units, that is thirtytwo plus three which is thirtyfive. This means that 10_{b} is one b and zero units. Thus the value of 10_{b} is the value of the base b. Hence if b = 8 as above then 10_{8} is eight. Hence in your question above 10_{b} is the value of the base, 11_{b} is the value of the base, plus one and 12_{b} is the value of the base, plus 2. So if the base is 8 then 10_{8} is eight, 11_{8} is nine and 12_{8} is ten. I hope this helps,
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 