Use long division to convert 5 and 3/16 to a decimal a squiggly lines 5.3 B 5.36 c 0.1875 d 5.1875

Answer 1

To convert the mixed number \(5 \frac{3}{16}\) to a decimal using long division, we first need to convert the fraction \( \frac{3}{16} \) to its decimal form.

Step 1: Perform Long Division for \( \frac{3}{16} \)

1. Set up the long division of \(3 \div 16\).
2. Since 16 is greater than 3, we know that \(16\) goes into \(3\) zero times. So we write \(0.\) in the quotient and add a decimal point, bringing down a zero (making it \(30\)).
3. Determine how many times \(16\) goes into \(30\):
   • \(16 \times 1 = 16\) (it fits once)
   • Write \(1\) in the quotient.
   • Subtract \(16\) from \(30\): \(30 - 16 = 14\).
4. Bring down another zero, making it \(140\).
5. Determine how many times \(16\) goes into \(140\):
   • \(16 \times 8 = 128\) (it fits eight times)
   • Write \(8\) in the quotient.
   • Subtract \(128\) from \(140\): \(140 - 128 = 12\).
6. Bring down another zero, making it \(120\).
7. Determine how many times \(16\) goes into \(120\):
   • \(16 \times 7 = 112\) (it fits seven times)
   • Write \(7\) in the quotient.
   • Subtract \(112\) from \(120\): \(120 - 112 = 8\).
8. Bring down another zero, making it \(80\).
9. Determine how many times \(16\) goes into \(80\):
   • \(16 \times 5 = 80\) (it fits five times)
   • Write \(5\) in the quotient.
   • Subtract \(80\) from \(80\): \(80 - 80 = 0\).

Result of Long Division

Combining all the parts of the quotient, we have:

\[ \frac{3}{16} = 0.1875 \]

Step 2: Add the Whole Number

Now, add the integral part \(5\) to the decimal part \(0.1875\):

\[ 5 + 0.1875 = 5.1875 \]

Final Answer

Thus, the decimal form of \(5 \frac{3}{16}\) is:

\[ \boxed{5.1875} \]

So the correct choice from your options is \(d\) \(5.1875\).