When `(55)_(10)` represented in base 25 then the expression is

Options

A. `(25)_(25)`
B. `(35)_(25)`
C. `(55)_(25)`
D. none of these

Answer

To convert the decimal number \( (55)_{10} \) into base \( 25 \), we will follow these steps:

### Step 1: Divide the number by the base
We start by dividing \( 55 \) by \( 25 \).

\[ 55 \div 25 = 2 \quad \text{(quotient)} \]
\[ 55 - (25 \times 2) = 5 \quad \text{(remainder)} \]

### Step 2: Record the remainder
The remainder from the division is \( 5 \).

### Step 3: Divide the quotient by the base
Next, we take the quotient \( 2 \) and divide it by \( 25 \).

\[ 2 \div 25 = 0 \quad \text{(quotient)} \]
\[ 2 - (25 \times 0) = 2 \quad \text{(remainder)} \]

### Step 4: Record the remainder
The remainder from this division is \( 2 \).

### Step 5: Write the base 25 representation
Now, we have the remainders from the divisions: the first remainder (from the first division) is \( 5 \) and the second remainder (from the second division) is \( 2 \).

To write the number in base \( 25 \), we read the remainders in reverse order:

\[ (25)_{25} = (25)_{10} \text{ is represented as } (25)_{25} = 25 \]

Thus, the representation of \( (55)_{10} \) in base \( 25 \) is \( (25)_{25} \).

### Final Answer
The expression of \( (55)_{10} \) in base \( 25 \) is \( (25)_{25} \).

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