We made this question unnecessarily hard for you, as we shall explain below. But look , our first octal numbers, starting with 0, were:
08, 18, 28, 38, 48, 58, 68, 78.
Except for the subscripts, these are the same as the equivalent decimal numbers. When we had counted up to eight we reached the first difference in the two systems. Eight is written in octal as 108. We can check that this is correct by expanding:
108 = 1(81) + 0(80) = 1(8) + 0(1) = 810.
What we wanted you to discover was that in the octal system we are not going to need any single digits larger than 7. We don’t use the 8 or 9 in the octal system, except for the subscript 8 that identifies the number as an octal number.
Now, if we don’t use the digits 8 and 9 in the octal system, we can’t write the quantity nine as 98. So we do just what we do in the decimal system to get to the next number beyond 10. We add 1 to the right-hand digit, which is the coefficient of the base raised to the 0 power:
decimaloctal
1010
= ten
+ 1101110
= eleven
108
= eight
+ 18118
= nine
