To convert \( 5 \frac{3}{16} \) to a decimal using long division, follow these steps:
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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.
- Step 1: How many times does 16 go into 83? It goes 5 times because \( 16 \times 5 = 80 \).
- Step 2: Subtract 80 from 83, which gives you 3.
- Step 3: You can now consider this as \( 3. \) You add a decimal point and a zero (making it 30) and continue.
- Step 4: How many times does 16 go into 30? It goes 1 time because \( 16 \times 1 = 16 \).
- Step 5: Subtract 16 from 30, which gives you 14.
- Step 6: Bring down another 0, making it 140.
- Step 7: How many times does 16 go into 140? It goes 8 times because \( 16 \times 8 = 128 \).
- Step 8: Subtract 128 from 140, which gives you 12.
- Step 9: Bring down another 0, making it 120.
- Step 10: How many times does 16 go into 120? It goes 7 times because \( 16 \times 7 = 112 \).
- Step 11: Subtract 112 from 120, which gives you 8.
- Step 12: Bring down another 0, making it 80.
- Step 13: How many times does 16 go into 80? It goes 5 times because \( 16 \times 5 = 80 \).
- Step 14: Subtract 80 from 80, which gives you 0.
So, completing the long division, we find that: \[ 83 \div 16 = 5.1875 \]
Thus, converting \( 5 \frac{3}{16} \) to a decimal gives \( 5.1875 \).
The correct response is: 5.1875.