Write the decimal representations of the following decimal numbers:
`(8)/(11)`

Answer

To find the decimal representation of the fraction \( \frac{8}{11} \), we will perform long division. Here’s a step-by-step solution:

### Step 1: Set up the division
We need to divide 8 by 11. Since 8 is less than 11, we will place a decimal point and add a zero to 8, making it 80.

### Step 2: Determine how many times 11 fits into 80
11 goes into 80 a total of 7 times because \( 11 \times 7 = 77 \).

### Step 3: Subtract to find the remainder
Now, we subtract 77 from 80:
\[ 80 - 77 = 3 \]
So, we have a remainder of 3.

### Step 4: Bring down another zero
Next, we bring down another zero, making it 30.

### Step 5: Determine how many times 11 fits into 30
11 goes into 30 a total of 2 times because \( 11 \times 2 = 22 \).

### Step 6: Subtract to find the new remainder
Now, we subtract 22 from 30:
\[ 30 - 22 = 8 \]
So, we have a remainder of 8 again.

### Step 7: Repeat the process
We bring down another zero, making it 80 again. We see that we are back to where we started.

### Step 8: Identify the repeating pattern
Since we previously found that 11 goes into 80 a total of 7 times, we can see that the decimal will repeat.

Thus, the decimal representation of \( \frac{8}{11} \) is:
\[ 0.727272\ldots \]
We can express this as \( 0.\overline{72} \), indicating that "72" repeats indefinitely.

### Final Answer
The decimal representation of \( \frac{8}{11} \) is \( 0.\overline{72} \).

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