Convert `(725)_(10)` to hexadecimal.

Answer

To convert the decimal number \( (725)_{10} \) to hexadecimal, we can follow these steps:

### Step 1: Divide the number by 16
We start by dividing 725 by 16.

\[ 725 \div 16 = 45 \quad \text{(Quotient)} \]
\[ 725 \mod 16 = 5 \quad \text{(Remainder)} \]

### Step 2: Write down the remainder
The remainder from this division is 5. In hexadecimal, this is represented as \( 5 \).

### Step 3: Divide the quotient by 16
Next, we take the quotient (45) and divide it by 16 again.

\[ 45 \div 16 = 2 \quad \text{(Quotient)} \]
\[ 45 \mod 16 = 13 \quad \text{(Remainder)} \]

### Step 4: Write down the remainder
The remainder from this division is 13. In hexadecimal, 13 is represented as \( D \).

### Step 5: Divide the new quotient by 16
Now, we take the new quotient (2) and divide it by 16.

\[ 2 \div 16 = 0 \quad \text{(Quotient)} \]
\[ 2 \mod 16 = 2 \quad \text{(Remainder)} \]

### Step 6: Write down the remainder
The remainder from this division is 2. In hexadecimal, this is represented as \( 2 \).

### Step 7: Compile the hexadecimal number
Now we compile the hexadecimal digits from the remainders we obtained. We write them from the last remainder to the first:

- Last remainder: \( 2 \)
- Second remainder: \( D \)
- First remainder: \( 5 \)

Thus, the hexadecimal representation of \( (725)_{10} \) is \( (2D5)_{16} \).

### Final Answer
\[ (725)_{10} = (2D5)_{16} \]

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