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

Question

Responses

≈5.3
approximately equals 5.3

5.36
5.36

5.1875
5.1875

0.1875

Answer 1

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. Perform long division to divide 83 by 16:

   • 16 goes into 83 five times (since \( 16 \times 5 = 80 \)).
   • Subtract \( 80 \) from \( 83 \), which leaves a remainder of \( 3 \).

3. Continue with the decimal:

   • Add a decimal point and a zero to the remainder to make it 30.
   • Now divide \( 30 \) by \( 16 \). 16 goes into 30 once (since \( 16 \times 1 = 16 \)).
   • Subtract \( 16 \) from \( 30 \), which leaves a remainder of \( 14 \).

4. Continue the process:

   • Bring down another 0 to make it \( 140 \).
   • 16 goes into \( 140 \) eight times (since \( 16 \times 8 = 128 \)).
   • Subtract \( 128 \) from \( 140 \), which leaves a remainder of \( 12 \).

5. Repeat again:

   • Bring down another 0 to make it \( 120 \).
   • 16 goes into \( 120 \) seven times (since \( 16 \times 7 = 112 \)).
   • Subtract \( 112 \) from \( 120 \), which leaves a remainder of \( 8 \).

6. One more time:

   • Bring down another 0 to make it \( 80 \).
   • 16 goes into \( 80 \) five times (since \( 16 \times 5 = 80 \)).
   • Subtract \( 80 \) from \( 80 \), which leaves a remainder of \( 0 \).

At this point, we have: \[ 83 \div 16 = 5.1875 \]

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

The correct response is: 5.1875