Convert `(0.03125)_(10)` to base 16.

Answer

To convert the decimal fraction \( (0.03125)_{10} \) to base 16, we will follow these steps:

### Step 1: Multiply by 16
Take the decimal fraction \( 0.03125 \) and multiply it by 16.

\[ 0.03125 \times 16 = 0.5 \]

### Step 2: Separate the Whole Number
The result from Step 1 is \( 0.5 \). The whole number part is \( 0 \) and the fractional part is \( 0.5 \).

### Step 3: Record the Whole Number
The whole number part \( 0 \) is the first digit in our hexadecimal representation.

### Step 4: Repeat the Process
Now take the fractional part \( 0.5 \) and multiply it by 16 again.

\[ 0.5 \times 16 = 8.0 \]

### Step 5: Separate the Whole Number Again
The whole number part is now \( 8 \) and the fractional part is \( 0.0 \).

### Step 6: Record the Whole Number
The whole number part \( 8 \) is the next digit in our hexadecimal representation.

### Step 7: Stop the Process
Since the fractional part is now \( 0.0 \), we can stop the process here.

### Final Result
Combining the whole number parts we recorded, we have:

\[ (0.03125)_{10} = (0.08)_{16} \]