Answer:
The problem here is that 9 is not a valid number representation in base 7, all digits of the numbers in base 7 can be 0,1,2,3,4,5 and 6.
The correct representation in base 7 is [tex]112_7[/tex]
Step-by-step explanation:
In order to convert from decimal number to other base, we can work with division methods, but to use the remainder to write the digits of the number on the new base.
So we can start with 58 divided by 7, that give us 8 as result, with a remainder of 2.
[tex]8(7)+2 = 58[/tex]
Thus the remainder 2 is the first digit of the number on base 7.
Then we repeat the process using the quotient, 8 divided by 7 is 1 with remainder 1, so the next digit is the remainder 1, and the last third digit counting from the right is the quotient 1, so we get
[tex]58=112_7[/tex]
That is the right representation of 58 in base 7, and notice that the number [tex]109_7[/tex] was not right, since it had a 9 and that 9 is not a valid digit in base 7, we could have divided 9 by 7 to get result 1 and remainder 2, to fix it to get the number [tex]112_7[/tex]
