Express each of the following as a recurring decimal :
`5/6`

Answer

To express the fraction \( \frac{5}{6} \) as a recurring decimal, we will perform the division of 5 by 6 step by step.

### Step 1: Set up the division
We need to divide 5 by 6. Since 5 is less than 6, we cannot divide it directly. We will start by adding a decimal point and a zero.

### Step 2: Convert to a decimal
We can write 5 as 5.0. Now we divide 5.0 by 6.

### Step 3: Perform the division
- 6 goes into 50 (the first two digits after the decimal) 8 times because \( 6 \times 8 = 48 \).
- Subtract 48 from 50, which gives us a remainder of 2.

### Step 4: Bring down the next zero
Now, we bring down another 0, making it 20.

### Step 5: Divide again
- 6 goes into 20 three times because \( 6 \times 3 = 18 \).
- Subtract 18 from 20, which gives us a remainder of 2 again.

### Step 6: Repeat the process
- Bring down another 0, making it 20 again.
- 6 goes into 20 three times, giving us 18 again, and we are left with a remainder of 2.

### Step 7: Identify the recurring part
This process will continue indefinitely, with the remainder always being 2 and the quotient being 3. Thus, we see that the digit 3 will keep repeating.

### Final Result
Therefore, we can express \( \frac{5}{6} \) as a recurring decimal:
\[ \frac{5}{6} = 0.83\overline{3} \]
This means that the decimal is \( 0.83333...\) where the digit 3 repeats indefinitely.