Question

112 base 3 to 8

Answer 1

To convert the number \(112\) from base \(3\) to base \(8\), we can first convert it from base \(3\) to base \(10\) (decimal), and then from base \(10\) to base \(8\).

### Step 1: Convert from base 3 to base 10

The number \(112\) in base \(3\) can be expanded as follows:

\[
1 \times 3^2 + 1 \times 3^1 + 2 \times 3^0
\]

Calculating that:

\[
1 \times 9 + 1 \times 3 + 2 \times 1 = 9 + 3 + 2 = 14
\]

So, \(112\) base \(3\) is equal to \(14\) in base \(10\).

### Step 2: Convert from base 10 to base 8

Now, we will convert \(14\) from base \(10\) to base \(8\). We can do this by repeatedly dividing by \(8\) and keeping track of the remainders.

1. \(14 \div 8 = 1\) with a remainder of \(6\).
2. \(1 \div 8 = 0\) with a remainder of \(1\).

Now we read the remainders from bottom to top:

The base \(8\) representation of \(14\) is \(16\).

### Conclusion

Thus, \(112\) in base \(3\) is equal to \(16\) in base \(8\).

\[
\text{Answer: } 16 \text{ (base 8)}
\]