Answer:
Therefore, the base-6 representation of 1407 is 1303.
Explanation:
To convert the decimal numeral 1407 to base 6, we can use the following steps:
Divide 1407 by 6 and store the quotient and the remainder.
Repeat the division process with the quotient until the quotient is 0.
Write down the remainders in the reverse order to get the base-6 representation of 1407.
So, the steps would look like this:
1407 ÷ 6 = 234 with a remainder of 3
234 ÷ 6 = 39 with a remainder of 0
39 ÷ 6 = 6 with a remainder of 3
6 ÷ 6 = 1 with a remainder of 0
1 ÷ 6 = 0 with a remainder of 1
Writing down the remainders in the reverse order, we get: 1407(10) = 1303_6.
Therefore, the base-6 representation of 1407 is 1303.