By actural division , express each of the following as a repeating decimal :
`101/15`

Answer

To express \( \frac{101}{15} \) as a repeating decimal using actual division, we will follow these steps:

### Step 1: Set up the division
We need to divide 101 by 15.

### Step 2: Perform the division
1. **Divide 101 by 15**:
- 15 goes into 101 six times because \( 15 \times 6 = 90 \).
- Write down 6 and subtract 90 from 101.
- \( 101 - 90 = 11 \) (This is the remainder).

### Step 3: Add a decimal point
Since we have a remainder, we will add a decimal point and a zero to the remainder to continue the division.

### Step 4: Continue the division
2. **Now divide 110 by 15** (adding a zero to the remainder):
- 15 goes into 110 seven times because \( 15 \times 7 = 105 \).
- Write down 7 and subtract 105 from 110.
- \( 110 - 105 = 5 \) (This is the new remainder).

3. **Add another zero to the remainder**:
- Now we have 50.
- 15 goes into 50 three times because \( 15 \times 3 = 45 \).
- Write down 3 and subtract 45 from 50.
- \( 50 - 45 = 5 \) (This is the new remainder again).

### Step 5: Identify the repeating part
4. **Notice the pattern**:
- We have a remainder of 5 again, which means we will repeat the previous steps.
- This indicates that the digits "3" will keep repeating.

### Final Result
Putting it all together, we have:
- The whole number part is 6.
- The decimal part is 0.7 (with 3 repeating).

Thus, we can express \( \frac{101}{15} \) as:
\[ 6.7\overline{3} \]
or \( 6.73333...\) where the 3 repeats indefinitely.