To convert the mixed number \( 5 \frac{3}{16} \) to a decimal using long division, first, we need to separate the whole number from the fraction.
- The whole number is \( 5 \).
- For the fraction \( \frac{3}{16} \), we will divide \( 3 \) by \( 16 \).
Now, perform the long division of \( 3 \div 16 \):
- \( 16 \) does not go into \( 3 \), so we place a \( 0 \) and add a decimal point. We can then treat \( 3 \) as \( 3.000 \) (adding decimal places).
Now we have:
- \( 16 \) goes into \( 30 \) once, giving us \( 16 \). Subtract \( 16 \) from \( 30 \) to get \( 14 \).
- Bring down the next \( 0 \) to make it \( 140 \).
Now check how many times \( 16 \) goes into \( 140 \):
- \( 16 \) goes into \( 140 \) \( 8 \) times, giving us \( 128 \). Subtract \( 128 \) from \( 140 \) to get \( 12 \).
- Bring down the next \( 0 \) to make it \( 120 \).
Now check how many times \( 16 \) goes into \( 120 \):
- \( 16 \) goes into \( 120 \) \( 7 \) times, giving us \( 112 \). Subtract \( 112 \) from \( 120 \) to get \( 8 \).
- Bring down the next \( 0 \) to make it \( 80 \).
Now check how many times \( 16 \) goes into \( 80 \):
- \( 16 \) goes into \( 80 \) \( 5 \) times, giving us \( 80 \). Subtract \( 80 \) from \( 80 \) to get \( 0 \).
Now we have finished dividing. Synthesizing this:
\[ 3 \div 16 = 0.1875 \]
Now, combine this result with the whole number part:
\[ 5 + 0.1875 = 5.1875 \]
Thus, converting \( 5 \frac{3}{16} \) to a decimal gives us \( 5.1875 \).
The correct response is: 5.1875