Convert each of the following into a decimal fraction:
Q (i)`27/4`
(ii)`2 5/8`

Answer

To convert the given fractions into decimal fractions, we will follow these steps:

### Part (i): Convert `27/4` into a decimal fraction

1. **Divide 27 by 4**:
- Start by dividing 27 by 4.
- 4 goes into 27 a total of 6 times (since 4 x 6 = 24).
- Write down 6.

2. **Subtract to find the remainder**:
- Subtract 24 from 27, which gives us a remainder of 3.

3. **Add a decimal point and a zero**:
- Since we have a remainder, we add a decimal point to our answer and a zero to the remainder, making it 30.

4. **Divide again**:
- Now divide 30 by 4.
- 4 goes into 30 a total of 7 times (since 4 x 7 = 28).
- Write down 7.

5. **Subtract again**:
- Subtract 28 from 30, which gives us a remainder of 2.

6. **Add another zero**:
- Add another zero to the remainder, making it 20.

7. **Divide again**:
- Now divide 20 by 4.
- 4 goes into 20 a total of 5 times (since 4 x 5 = 20).
- Write down 5.

8. **Final remainder**:
- Subtract 20 from 20, which gives us a remainder of 0.

9. **Final answer**:
- Therefore, `27/4` as a decimal fraction is **6.75**.

### Part (ii): Convert `2 5/8` into a decimal fraction

1. **Convert the mixed number to an improper fraction**:
- Multiply the whole number (2) by the denominator (8):
- 2 x 8 = 16.
- Add the numerator (5) to this product:
- 16 + 5 = 21.
- So, `2 5/8` can be written as `21/8`.

2. **Divide 21 by 8**:
- Start by dividing 21 by 8.
- 8 goes into 21 a total of 2 times (since 8 x 2 = 16).
- Write down 2.

3. **Subtract to find the remainder**:
- Subtract 16 from 21, which gives us a remainder of 5.

4. **Add a decimal point and a zero**:
- Since we have a remainder, we add a decimal point to our answer and a zero to the remainder, making it 50.

5. **Divide again**:
- Now divide 50 by 8.
- 8 goes into 50 a total of 6 times (since 8 x 6 = 48).
- Write down 6.

6. **Subtract again**:
- Subtract 48 from 50, which gives us a remainder of 2.

7. **Add another zero**:
- Add another zero to the remainder, making it 20.

8. **Divide again**:
- Now divide 20 by 8.
- 8 goes into 20 a total of 2 times (since 8 x 2 = 16).
- Write down 2.

9. **Final remainder**:
- Subtract 16 from 20, which gives us a remainder of 4.

10. **Add another zero**:
- Add another zero to the remainder, making it 40.

11. **Divide again**:
- Now divide 40 by 8.
- 8 goes into 40 a total of 5 times (since 8 x 5 = 40).
- Write down 5.

12. **Final remainder**:
- Subtract 40 from 40, which gives us a remainder of 0.

13. **Final answer**:
- Therefore, `2 5/8` as a decimal fraction is **2.625**.

### Summary of Answers:
- (i) `27/4` = **6.75**
- (ii) `2 5/8` = **2.625**