Convert `(8976)_(10)` in base 9.

Answer

To convert the decimal number \( (8976)_{10} \) to base 9, we can follow these steps:

### Step 1: Divide the number by the base
We start by dividing the number \( 8976 \) by \( 9 \).

\[ 8976 \div 9 = 996 \quad \text{with a remainder of } 6 \]

### Step 2: Record the remainder
The remainder from the division is \( 6 \). This will be the least significant digit (rightmost) in the base 9 representation.

### Step 3: Repeat the division with the quotient
Now, we take the quotient \( 996 \) and divide it by \( 9 \).

\[ 996 \div 9 = 110 \quad \text{with a remainder of } 6 \]

### Step 4: Record the next remainder
The remainder is \( 6 \). We will record this next.

### Step 5: Continue dividing the quotient
Next, we take the quotient \( 110 \) and divide it by \( 9 \).

\[ 110 \div 9 = 12 \quad \text{with a remainder of } 2 \]

### Step 6: Record the next remainder
The remainder is \( 2 \). We will record this next.

### Step 7: Divide the new quotient
Now, we take the quotient \( 12 \) and divide it by \( 9 \).

\[ 12 \div 9 = 1 \quad \text{with a remainder of } 3 \]

### Step 8: Record the next remainder
The remainder is \( 3 \). We will record this next.

### Step 9: Final division
Finally, we take the quotient \( 1 \) and divide it by \( 9 \).

\[ 1 \div 9 = 0 \quad \text{with a remainder of } 1 \]

### Step 10: Record the last remainder
The remainder is \( 1 \). We will record this last.

### Step 11: Compile the remainders
Now we compile all the remainders from the last division to the first:

- From the last division: \( 1 \)
- From the previous division: \( 3 \)
- From the previous division: \( 2 \)
- From the previous division: \( 6 \)
- From the first division: \( 6 \)

Thus, the base 9 representation of \( (8976)_{10} \) is:

\[ (13266)_{9} \]