Convert each of the following fractions into a decimal :
`2(9)/16`

Answer

To convert the mixed fraction \( 2 \frac{9}{16} \) into a decimal, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction consists of a whole number and a proper fraction. To convert it into an improper fraction, we use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]

For \( 2 \frac{9}{16} \):

\[ \text{Improper Fraction} = \left(2 \times 16 + 9\right) / 16 = \left(32 + 9\right) / 16 = 41 / 16 \]

### Step 2: Perform long division to convert the improper fraction to a decimal
Now we need to divide 41 by 16 using long division.

1. **Divide 41 by 16**:
- 16 goes into 41 two times (since \( 16 \times 2 = 32 \)).
- Write down 2.
- Subtract \( 32 \) from \( 41 \) to get a remainder of \( 9 \).

2. **Add a decimal point and a zero**:
- Since 9 is not divisible by 16, we add a decimal point and a zero, making it \( 90 \).

3. **Divide 90 by 16**:
- 16 goes into 90 five times (since \( 16 \times 5 = 80 \)).
- Write down 5.
- Subtract \( 80 \) from \( 90 \) to get a remainder of \( 10 \).

4. **Add another zero**:
- Again, since 10 is not divisible by 16, we add another zero, making it \( 100 \).

5. **Divide 100 by 16**:
- 16 goes into 100 six times (since \( 16 \times 6 = 96 \)).
- Write down 6.
- Subtract \( 96 \) from \( 100 \) to get a remainder of \( 4 \).

6. **Add another zero**:
- Since 4 is not divisible by 16, we add another zero, making it \( 40 \).

7. **Divide 40 by 16**:
- 16 goes into 40 two times (since \( 16 \times 2 = 32 \)).
- Write down 2.
- Subtract \( 32 \) from \( 40 \) to get a remainder of \( 8 \).

8. **Add another zero**:
- Since 8 is not divisible by 16, we add another zero, making it \( 80 \).

9. **Divide 80 by 16**:
- 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
- Write down 5.
- Subtract \( 80 \) from \( 80 \) to get a remainder of \( 0 \).

Now, we have completed the division.

### Final Result
Putting it all together, we find that:

\[ 2 \frac{9}{16} = 2.5625 \]