The decimal number system uses the characters 0, 1, 2, …., 8, 9, and the octal number system uses the characters 0, 1, 2, …., 6, 7. For example, the decimal number 12 (= 1 × 10¹ + 2 × 10⁰) is expressed as 14 1 0 (= 1 × 8¹ + 4 × 8⁰ ) in the octal number system.

The decimal number 108 in the octal number system is

The correct option is 154.

To convert a decimal number (base 10) to an octal number (base 8), we divide the decimal number by 8 repeatedly and record the remainders. The octal representation is then read from the last remainder to the first remainder (bottom to top).

Let's convert the decimal number 108 into the octal system step-by-step:

First, divide 108 by 8:
$108÷8=13$ with a remainder of 4.

Next, divide the quotient 13 by 8:
$13÷8=1$ with a remainder of 5.

Finally, divide the quotient 1 by 8:
$1÷8=0$ with a remainder of 1.

Writing the remainders from the last division to the first, we get: 1, 5, 4.

Therefore, the decimal number 108 in the octal number system is 154.

We can verify this result by expanding 154 in base 8:
$1\times 8^2+5\times 8^1+4\times 8^0=1\times 64+5\times 8+4\times 1$
$=64+40+4=108$