Convert the decimal to the given base.

12 to base six:

A. [tex]36_{\text{six}}[/tex]
B. [tex]20_{\text{six}}[/tex]
C. [tex]24_{\text{six}}[/tex]
D. [tex]8_{\text{six}}[/tex]



Answer :

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]