Write the decimal representations of the following rational numbers:
`(5)/(6)`

Answer

To find the decimal representation of the rational number \( \frac{5}{6} \), we can follow these steps:

### Step 1: Set up the division
We need to divide 5 by 6. Since 5 is smaller than 6, we will add a decimal point and a zero to 5, making it 5.0.

### Step 2: Perform the division
Now we divide 5.0 by 6:
- 6 goes into 50 (the first two digits after the decimal) a total of 8 times, because \( 6 \times 8 = 48 \).
- Write down 8 after the decimal point.

### Step 3: Subtract
Now subtract 48 from 50:
- \( 50 - 48 = 2 \).

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

### Step 5: Continue the division
Now divide 20 by 6:
- 6 goes into 20 a total of 3 times, because \( 6 \times 3 = 18 \).
- Write down 3 after the 8.

### Step 6: Subtract again
Now subtract 18 from 20:
- \( 20 - 18 = 2 \).

### Step 7: Repeat the process
Again, bring down another 0, making it 20.
- Divide 20 by 6 again, which gives us another 3.
- Subtract 18 from 20 again, leaving us with 2.

### Step 8: Identify the repeating decimal
Since we keep getting a remainder of 2 and repeating the process, we see that the digit 3 will keep repeating. Therefore, we can write the decimal representation of \( \frac{5}{6} \) as \( 0.8333... \).

### Final Answer
We can denote the repeating decimal as \( 0.83\overline{3} \), where the bar indicates that the digit 3 repeats indefinitely.

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