Use long division to convert 5 3/16 to a decimal.(1 point) Responses 0.1875 0.1875 5.36 5.36 ≈5.3 approximately equals 5.3 5.1875 5.1875

To convert \( 5 \frac{3}{16} \) to a decimal using long division, follow these steps:

1. **Convert the mixed number to an improper fraction:**
\[
5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16}
\]

2. **Now, divide 83 by 16 using long division:**

Set up the long division:
- 16 goes into 83 a total of 5 times (since \( 16 \times 5 = 80 \)).
- Subtract \( 80 \) from \( 83 \) to get \( 3 \).

3. **Continue the division:**
- The remainder is \( 3 \), so we can write this as \( 5 \) and \( \frac{3}{16} \).
- Now we need to convert \( \frac{3}{16} \) into decimal form.
- Divide \( 3 \) by \( 16 \):

\[
3.0000 \div 16
\]
- 16 goes into 30 once (1), with a remainder of 14.
- Bring down the next 0, making it 140.
- 16 goes into 140 eight times (8), with a remainder of 12.
- Bring down the next 0, making it 120.
- 16 goes into 120 seven times (7), with a remainder of 8.
- Bring down the next 0, making it 80.
- 16 goes into 80 five times (5), with a remainder of 0.

So, \( \frac{3}{16} = 0.1875 \).

4. **Combine the whole number part with the decimal part:**
\[
5 + 0.1875 = 5.1875
\]

Thus, the decimal representation of \( 5 \frac{3}{16} \) is **5.1875**.