You are correct. Since 7 is the largest single numeral in the octal system, the number following
178 must be
208. We can always check this by expanding the octal numbers and converting to decimal:
178
= 1(81) + 7(80) = 1(8) + 7(1) = 1510;
208
= 2(81) + 0(80) = 2(8) + 0(1) = 1610.
Now we can count in octal as follows:
08, 18, ⋯, 78,
108, 118, ⋯, 178,
208, 218, ⋯,
308, ⋯,
408, ⋯,
508, ⋯,
608, ⋯,
708, ⋯, 778, ⋯,
where the dots stand for numbers that we aren’t taking the space to write, since you can see how to fill in the blanks for yourself.
