Question

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

5.36
5.36

0.1875
0.1875

≈5.3
approximately equals 5.3

5.1875

Answer 1

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

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

2. Now we divide 83 by 16 using long division.

- 16 goes into 83 five times because \( 16 \times 5 = 80 \).
- Subtract 80 from 83, which leaves us with a remainder of 3.

3. Now, we include the remainder. Since we want to convert to decimal, we can add a decimal point and zeros. We treat 83 as 83.0 when we continue the division.
- Bring down a 0 (making our current value 30).
- 16 goes into 30 once because \( 16 \times 1 = 16 \).
- Subtract 16 from 30, which gives us 14.

4. Bring down another 0 (making it 140).
- 16 goes into 140 eight times because \( 16 \times 8 = 128 \).
- Subtract 128 from 140, leaving a remainder of 12.

5. Bring down another 0 (making it 120).
- 16 goes into 120 seven times because \( 16 \times 7 = 112 \).
- Subtract 112 from 120, leaving a remainder of 8.

6. Bring down another 0 (making it 80).
- 16 goes into 80 five times because \( 16 \times 5 = 80 \).
- Subtract 80 from 80, leaving a remainder of 0.

Now, we can put together the results:
- The whole number part is 5.
- The decimal part we obtained is 0.1875.

Hence, \( 5 \frac{3}{16} \) as a decimal is:
\[
5 + 0.1875 = 5.1875
\]

Therefore, the correct answer is **5.1875**.