Answer:
The problem is that 4 is not a valid number representation for base 3, the digit numbers in base 3 can be 0, 1 and 2.
The correct representation is [tex]13=111_3[/tex]
Step-by-step explanation:
The idea to convert from decimal number into other base number is to work with division and to use the remainder to make the number on the new base, and to remember to avoid using the quotient as one of the digits on the new base until we get a quotient smaller than the base.
On this case we start dividing 13 by 3, the result is 4, but the remainder is 1, so the first digit on base 3 is the remainder 1.
Next we use the result which is 4 and we repeat the division by 3, we get 1 for the remainder that will make the second digit, and we also get 1 for the result which will be the third digit counting from right to left, thus we get
[tex]13=111_3[/tex]
So notice that stopping at 41 was the mistake we cannot have 4 in base 3.
