Answer :
To convert the fraction [tex]\(\frac{5}{16}\)[/tex] to a decimal, you need to perform long division, dividing 5 by 16. Let's go through the steps:
1. Set up the division: Place 5 inside the division bracket and 16 outside.
2. Perform the division:
- Since 16 doesn't go into 5, you need to add a decimal point and proceed by adding zeros to 5, making it 5.0000.
- Determine how many times 16 fits into 50. It fits 3 times (since 16 x 3 = 48).
- Write 3 above the division line, right after the decimal point. Subtract 48 from 50, which leaves a remainder of 2.
3. Bring down the next zero, making it 20:
- Determine how many times 16 fits into 20. It fits 1 time (since 16 x 1 = 16).
- Write 1 above the division line. Subtract 16 from 20, which leaves a remainder of 4.
4. Bring down the next zero, making it 40:
- Determine how many times 16 fits into 40. It fits 2 times (since 16 x 2 = 32).
- Write 2 above the division line. Subtract 32 from 40, which leaves a remainder of 8.
5. Bring down the last zero, making it 80:
- Determine how many times 16 fits into 80. It fits 5 times (since 16 x 5 = 80).
- Write 5 above the division line. Subtract 80 from 80, which leaves a remainder of 0.
So, the division shows that [tex]\(\frac{5}{16} = 0.3125\)[/tex].
This calculation matches the calculation shown in choice C:
[tex]\[
\begin{array}{r}
0.3125 \\
1 6 \longdiv { 5 0 0 0 0 } \\
-48 \\
\hline 20 \\
-16 \\
40 \\
-32 \\
\hline 80 \\
-\frac{80}{0}
\end{array}
\][/tex]
Therefore, the correct answer is choice C.
1. Set up the division: Place 5 inside the division bracket and 16 outside.
2. Perform the division:
- Since 16 doesn't go into 5, you need to add a decimal point and proceed by adding zeros to 5, making it 5.0000.
- Determine how many times 16 fits into 50. It fits 3 times (since 16 x 3 = 48).
- Write 3 above the division line, right after the decimal point. Subtract 48 from 50, which leaves a remainder of 2.
3. Bring down the next zero, making it 20:
- Determine how many times 16 fits into 20. It fits 1 time (since 16 x 1 = 16).
- Write 1 above the division line. Subtract 16 from 20, which leaves a remainder of 4.
4. Bring down the next zero, making it 40:
- Determine how many times 16 fits into 40. It fits 2 times (since 16 x 2 = 32).
- Write 2 above the division line. Subtract 32 from 40, which leaves a remainder of 8.
5. Bring down the last zero, making it 80:
- Determine how many times 16 fits into 80. It fits 5 times (since 16 x 5 = 80).
- Write 5 above the division line. Subtract 80 from 80, which leaves a remainder of 0.
So, the division shows that [tex]\(\frac{5}{16} = 0.3125\)[/tex].
This calculation matches the calculation shown in choice C:
[tex]\[
\begin{array}{r}
0.3125 \\
1 6 \longdiv { 5 0 0 0 0 } \\
-48 \\
\hline 20 \\
-16 \\
40 \\
-32 \\
\hline 80 \\
-\frac{80}{0}
\end{array}
\][/tex]
Therefore, the correct answer is choice C.
