To convert \( 5 \frac{3}{16} \) to a decimal using long division, follow these steps:
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First, convert the mixed number to an improper fraction: \[ 5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16} \]
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Now, divide \( 83 \) by \( 16 \) using long division.
- How many times does \( 16 \) go into \( 83 \)? It goes \( 5 \) times since \( 16 \times 5 = 80 \).
- Subtract \( 80 \) from \( 83 \):
\[ 83 - 80 = 3 \] - Now, we continue with \( 3 \).
- Bring down a zero to get \( 30 \).
- How many times does \( 16 \) go into \( 30 \)? It goes \( 1 \) time since \( 16 \times 1 = 16 \).
- Subtract \( 16 \) from \( 30 \):
\[ 30 - 16 = 14 \] - Bring down another zero to get \( 140 \).
- How many times does \( 16 \) go into \( 140 \)? It goes \( 8 \) times since \( 16 \times 8 = 128 \).
- Subtract \( 128 \) from \( 140 \):
\[ 140 - 128 = 12 \] - Bring down another zero to get \( 120 \).
- How many times does \( 16 \) go into \( 120 \)? It goes \( 7 \) times since \( 16 \times 7 = 112 \).
- Subtract \( 112 \) from \( 120 \):
\[ 120 - 112 = 8 \] - Bring down another zero to get \( 80 \).
- How many times does \( 16 \) go into \( 80 \)? It goes \( 5 \) times since \( 16 \times 5 = 80 \).
- Subtract \( 80 \) from \( 80 \):
\[ 80 - 80 = 0 \]
Putting all this together, you have the result of the division: \[ 83 \div 16 = 5.1875 \]
So, \( 5 \frac{3}{16} \) as a decimal is \( 5.1875 \).
The correct response is: 5.1875