Convert `5//11` into decimal form .

Answer

To convert \( \frac{5}{11} \) into decimal form, we can follow these steps:

### Step 1: Set up the division
We will divide 5 by 11. Since 5 is less than 11, we will start by adding a decimal point and a zero to 5, making it 5.0 (or 50 when we consider the decimal point).

### Step 2: Perform the division
- **Divide 50 by 11**:
- 11 goes into 50 four times (since \( 11 \times 4 = 44 \)).
- Write down 4 after the decimal point.
- Subtract \( 44 \) from \( 50 \) to get \( 6 \).

### Step 3: Bring down the next zero
- Now we have \( 6 \). Bring down another zero to make it \( 60 \).

### Step 4: Continue the division
- **Divide 60 by 11**:
- 11 goes into 60 five times (since \( 11 \times 5 = 55 \)).
- Write down 5 next to the 4, making it \( 0.45 \).
- Subtract \( 55 \) from \( 60 \) to get \( 5 \).

### Step 5: Repeat the process
- Bring down another zero to make it \( 50 \) again.
- Repeat the division:
- 11 goes into 50 four times (again, \( 44 \)).
- Subtract \( 44 \) from \( 50 \) to get \( 6 \).
- Bring down another zero to make it \( 60 \).
- 11 goes into 60 five times (again, \( 55 \)).
- Subtract \( 55 \) from \( 60 \) to get \( 5 \).

### Step 6: Identify the repeating pattern
We see that the digits \( 45 \) are repeating. Therefore, we can represent the decimal as:
\[ \frac{5}{11} = 0.454545\ldots \]
This can be written as \( 0.\overline{45} \), indicating that \( 45 \) repeats indefinitely.

### Final Answer
Thus, the decimal form of \( \frac{5}{11} \) is:
\[ 0.\overline{45} \]

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