To convert the decimal number 12 to base six, follow these steps:
1. Identify the highest power of 6 that fits into 12:
- [tex]\(6^0 = 1\)[/tex]
- [tex]\(6^1 = 6\)[/tex]
- [tex]\(6^2 = 36\)[/tex]
Since [tex]\(6^2 = 36\)[/tex] is greater than 12, we use [tex]\(6^1 = 6\)[/tex] as the highest power.
2. Determine how many times [tex]\(6^1\)[/tex] can fit into 12:
- [tex]\(12 \div 6 = 2\)[/tex] with no remainder.
This tells us that 12 contains two 6's.
3. Calculate the remainder after dividing by the highest power of 6:
- [tex]\(12 - (2 \times 6) = 12 - 12 = 0\)[/tex]
4. Since we are only left with the remainder 0, we have no need to divide further.
5. Combine the coefficients thus found:
- The coefficient for [tex]\(6^1\)[/tex] is 2 and for [tex]\(6^0\)[/tex] is 0.
Therefore, when combining these coefficients, the conversion results in:
[tex]\[ 12_{\text{ten}} = 20_{\text{six}} \][/tex]
So, the correct conversion of decimal 12 to base six is:
[tex]\[ 20_{\text{six}} \][/tex]
