Question

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

5.1875
5.1875

5.36
5.36

0.1875
0.1875

≈5.3

Answer 1

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

1. **Convert the mixed number to an improper fraction**:
To do this, multiply the whole number by the denominator and add the numerator.
\[
5 \frac{3}{16} = \frac{(5 \times 16) + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16}
\]

2. **Perform long division to convert \( \frac{83}{16} \) to a decimal**:
Divide 83 by 16.

- 16 goes into 83 a total of 5 times (since \( 16 \times 5 = 80 \)).
- Subtract 80 from 83 which leaves you with a remainder of 3.
\[
83 - 80 = 3
\]

Now bring down a zero to continue the division.
- Now you're dividing 30 by 16.
- 16 goes into 30 once (since \( 16 \times 1 = 16 \)).
- Subtract 16 from 30 which leaves you with a remainder of 14.
\[
30 - 16 = 14
\]

Bring down another zero to get 140.
- 16 goes into 140 eight times (since \( 16 \times 8 = 128 \)).
- Subtract 128 from 140 which leaves you with a remainder of 12.
\[
140 - 128 = 12
\]

Bring down another zero to get 120.
- 16 goes into 120 seven times (since \( 16 \times 7 = 112 \)).
- Subtract 112 from 120 which leaves you with a remainder of 8.
\[
120 - 112 = 8
\]

Bring down another zero to get 80.
- 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
- Subtract 80 from 80 which leaves you with a remainder of 0.
\[
80 - 80 = 0
\]

3. **Combine the results**:
From the division, we have:
- \( 5 \) (the integer part),
- \( 1 \) (from the first decimal place),
- \( 8 \) (from the second decimal place),
- \( 7 \) (from the third decimal place),
- \( 5 \) (from the fourth decimal place).

Thus, \( 5 \frac{3}{16} = 5.1875 \).

So the answer is \( \boxed{5.1875} \).