Answer:
To represent the decimal 145 in base thirteen, we need to find the value of each digit in the base thirteen system.
In base thirteen, the digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C, where A represents 10, B represents 11, and C represents 12.
To convert 145 to base thirteen, we divide the number repeatedly by thirteen and write down the remainders, starting from the rightmost digit.
145 divided by 13 is 11 with a remainder of 2. So, the rightmost digit is 2, which corresponds to the letter 2 in base thirteen.
11 (quotient) divided by 13 is 0 with a remainder of 11. So, the next digit is 11, which corresponds to the letter B in base thirteen.
Since the quotient is now 0, we have finished the conversion.
Therefore, 145 in base thirteen is represented by the numeral 2B.
The correct answer is:
2B