To convert the fraction \( \frac{7}{16} \) to a decimal using long division, follow these steps:
- Set up the division. You want to divide 7 by 16.
- Since 7 is smaller than 16, first, we can rewrite it as \( 7.0000 \) (adding decimal places for division).
- Divide 16 into 70.
- 16 goes into 70 four times (since \( 16 \times 4 = 64 \)).
- Write down 4 with the decimal, which equals 0.4 in decimal form.
- Subtract \( 64 \) from \( 70 \) to get a remainder of \( 6 \).
- Bring down the next zero, making it \( 60 \).
- Divide 16 into 60.
- 16 goes into 60 three times (since \( 16 \times 3 = 48 \)).
- Write down 3 after the 4, so far you have 0.43.
- Subtract \( 48 \) from \( 60 \) to get a remainder of \( 12 \).
- Bring down the next zero, making it \( 120 \).
- Divide 16 into 120.
- 16 goes into 120 seven times (since \( 16 \times 7 = 112 \)).
- Write down 7, so far you have 0.437.
- Subtract \( 112 \) from \( 120 \) to get a remainder of \( 8 \).
- Bring down another zero, making it \( 80 \).
- Divide 16 into 80.
- 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
- Write down 5, so far you have 0.4375.
- Subtract \( 80 \) from \( 80 \) to get a remainder of \( 0 \).
So, \( \frac{7}{16} = 0.4375 \).
Finally, to find the decimal for the mixed number \( 2 \frac{7}{16} \), we add \( 2 \) to \( 0.4375 \):
\[ 2 + 0.4375 = 2.4375 \]
Thus, \( 2 \frac{7}{16} \) as a decimal is \( 2.4375 \).
The correct response is: 2.4375.