Question

Use long division to convert 5 3/16 to a decimal.(1 point)
Responses

5.36
5.36

0.1875
0.1875

5.1875
5.1875

≈5.3

Answer 1

To convert \( 5 \frac{3}{16} \) to a decimal using long division, we will first convert the mixed number to an improper fraction and then divide:

1. **Convert \( 5 \frac{3}{16} \) to an improper fraction:**

\[
5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16}
\]

2. **Now, perform the division \( 83 \div 16 \):**

- **How many times does 16 go into 83?**
- \( 16 \times 5 = 80 \), so it goes 5 times.
- **Calculate the remainder:**
\[
83 - 80 = 3
\]
- So, \( 83 \div 16 = 5 \) with a remainder of 3.

3. **Now we need to convert the remainder into a decimal:**
- Take the remainder (3), and append a decimal point, making it \( 3.0 \).
- We can rewrite \( 3.0 \div 16 \) and divide:
- \( 16 \) goes into \( 30 \): It goes \( 1 \) time (because \( 16 \times 1 = 16 \)).
- The remainder is \( 30 - 16 = 14 \).
- Now take down another \( 0 \), making it \( 140 \).
- \( 16 \) goes into \( 140 \) \( 8 \) times (because \( 16 \times 8 = 128 \)).
- The remainder is \( 140 - 128 = 12 \).
- Take down another \( 0 \), making it \( 120 \).
- \( 16 \) goes into \( 120 \) \( 7 \) times (because \( 16 \times 7 = 112 \)).
- The remainder is \( 120 - 112 = 8 \).
- Take down another \( 0 \), making it \( 80 \).
- \( 16 \) goes into \( 80 \) \( 5 \) times (because \( 16 \times 5 = 80 \)).
- The remainder is \( 80 - 80 = 0 \).

Thus, when we combine the results, we have:

\[
83 \div 16 = 5.1875
\]

The complete decimal representation of \( 5 \frac{3}{16} \) is \( 5.1875 \).

Therefore, the correct answer is:

**5.1875**