Answer :
To convert the fraction [tex]\(\frac{13}{16}\)[/tex] to a decimal, you should perform a division where 13 is divided by 16. Here is a step-by-step explanation of how to do this:
1. Set up the division: Place 13 as the numerator (inside the division bracket) and 16 as the denominator (outside the division bracket).
2. Perform the division:
- Since 13 is smaller than 16, you start by adding a decimal point and a zero to the 13 (making it 130) and place a decimal point in the quotient directly above.
- Now divide 16 into 130, which goes 8 times because 16 times 8 is 128.
- Write 8 in the quotient, and subtract 128 from 130 to get a remainder of 2.
- Bring down another zero to make it 20. Now divide 16 into 20, which goes 1 time because 16 times 1 is 16.
- Write 1 in the quotient, and subtract 16 from 20 to get a remainder of 4.
- Bring down another zero to make it 40. Now divide 16 into 40, which goes 2 times because 16 times 2 is 32.
- Write 2 in the quotient, and subtract 32 from 40 to get a remainder of 8.
- Bring down another zero to make it 80. Now divide 16 into 80, which goes 5 times because 16 times 5 is 80.
- Write 5 in the quotient, and subtract 80 from 80 to get a remainder of 0.
3. Conclusion: The decimal representation is complete when the remainder reaches 0.
Thus, [tex]\(\frac{13}{16}\)[/tex] converted to a decimal is [tex]\(0.8125\)[/tex].
Among the given options, option B correctly demonstrates the steps described:
[tex]\[
\begin{array}{r}
8125 \\
\text{16) } 130000 \\
-128 \\
\hline
20 \\
-16 \\
\hline
40 \\
-32 \\
\hline
80 \\
-80 \\
\hline
0
\end{array}
\][/tex]
This shows that the decimal representation of [tex]\(\frac{13}{16}\)[/tex] is [tex]\(0.8125\)[/tex].
1. Set up the division: Place 13 as the numerator (inside the division bracket) and 16 as the denominator (outside the division bracket).
2. Perform the division:
- Since 13 is smaller than 16, you start by adding a decimal point and a zero to the 13 (making it 130) and place a decimal point in the quotient directly above.
- Now divide 16 into 130, which goes 8 times because 16 times 8 is 128.
- Write 8 in the quotient, and subtract 128 from 130 to get a remainder of 2.
- Bring down another zero to make it 20. Now divide 16 into 20, which goes 1 time because 16 times 1 is 16.
- Write 1 in the quotient, and subtract 16 from 20 to get a remainder of 4.
- Bring down another zero to make it 40. Now divide 16 into 40, which goes 2 times because 16 times 2 is 32.
- Write 2 in the quotient, and subtract 32 from 40 to get a remainder of 8.
- Bring down another zero to make it 80. Now divide 16 into 80, which goes 5 times because 16 times 5 is 80.
- Write 5 in the quotient, and subtract 80 from 80 to get a remainder of 0.
3. Conclusion: The decimal representation is complete when the remainder reaches 0.
Thus, [tex]\(\frac{13}{16}\)[/tex] converted to a decimal is [tex]\(0.8125\)[/tex].
Among the given options, option B correctly demonstrates the steps described:
[tex]\[
\begin{array}{r}
8125 \\
\text{16) } 130000 \\
-128 \\
\hline
20 \\
-16 \\
\hline
40 \\
-32 \\
\hline
80 \\
-80 \\
\hline
0
\end{array}
\][/tex]
This shows that the decimal representation of [tex]\(\frac{13}{16}\)[/tex] is [tex]\(0.8125\)[/tex].
