Asked by optional
Use long division to convert 316
to a decimal.(1 point)
$$
to a decimal.(1 point)
$$
Answers
Answered by
oobleck
as written, the question makes no sense. It should be clear that they meant
3/16 = 0.1875
3/16 = 0.1875
Answered by
GPT-4o mini
To convert the whole number \( 316 \) to a decimal using long division, you can think of it as dividing \( 316 \) by \( 1 \). However, if you want to express \( 316 \) as a decimal, you simply write it as:
\[
316.0
\]
If you are looking to express \( 316 \) in a different format, such as converting it to a decimal with more precision, you can consider division by a number that changes its format.
But if we're performing long division to show how it behaves with decimal points, let's go through the process of dividing a larger number by \( 1 \):
1. Set up the long division where \( 316 \) is the dividend and \( 1 \) is the divisor:
\[
\begin{array}{r|l}
1 & 316.0 \\
\end{array}
\]
2. Perform the division:
- \( 1 \) goes into \( 3 \) (the first digit of \( 316 \)) \( 3 \) times. Multiply \( 1 \) by \( 3 \) getting \( 3 \).
- Subtract \( 3 \) from \( 3 \) which equals \( 0 \).
- Bring down the next digit, which is \( 1 \), making it \( 01 \).
- \( 1 \) goes into \( 01 \) \( 0 \) times, subtract \( 0 \) from \( 1 \) resulting in \( 1 \).
- Bring down the next digit, which is \( 6 \), making it \( 16 \).
- \( 1 \) goes into \( 16 \) \( 16 \) times.
- Multiply \( 1 \) by \( 16 \), getting \( 16 \).
- Subtract \( 16 \) from \( 16 \) resulting in \( 0 \).
So, combining all the results, we have:
\[
\begin{align*}
316 \div 1 & = 316 \\
\end{align*}
\]
Thus, simply put, \( 316 \) as a decimal is:
\[
316.0
\]
However, if you meant to convert something else into a decimal or perform a different operation, please clarify!
\[
316.0
\]
If you are looking to express \( 316 \) in a different format, such as converting it to a decimal with more precision, you can consider division by a number that changes its format.
But if we're performing long division to show how it behaves with decimal points, let's go through the process of dividing a larger number by \( 1 \):
1. Set up the long division where \( 316 \) is the dividend and \( 1 \) is the divisor:
\[
\begin{array}{r|l}
1 & 316.0 \\
\end{array}
\]
2. Perform the division:
- \( 1 \) goes into \( 3 \) (the first digit of \( 316 \)) \( 3 \) times. Multiply \( 1 \) by \( 3 \) getting \( 3 \).
- Subtract \( 3 \) from \( 3 \) which equals \( 0 \).
- Bring down the next digit, which is \( 1 \), making it \( 01 \).
- \( 1 \) goes into \( 01 \) \( 0 \) times, subtract \( 0 \) from \( 1 \) resulting in \( 1 \).
- Bring down the next digit, which is \( 6 \), making it \( 16 \).
- \( 1 \) goes into \( 16 \) \( 16 \) times.
- Multiply \( 1 \) by \( 16 \), getting \( 16 \).
- Subtract \( 16 \) from \( 16 \) resulting in \( 0 \).
So, combining all the results, we have:
\[
\begin{align*}
316 \div 1 & = 316 \\
\end{align*}
\]
Thus, simply put, \( 316 \) as a decimal is:
\[
316.0
\]
However, if you meant to convert something else into a decimal or perform a different operation, please clarify!
Answered by
GPT-4o mini
Thank you for the clarification! If you are looking to convert \( \frac{3}{16} \) to a decimal using long division, let's go through that process.
### Long Division of \( 3 \div 16 \):
1. **Set Up the Division**: Write \( 3 \) as the dividend and \( 16 \) as the divisor.
```
______________
16 | 3.000000
```
2. **Determine How Many Times 16 Goes into 3**:
- \( 16 \) goes into \( 3 \) \( 0 \) times, so we write \( 0 \) in the quotient. Since we need decimal division, we add a decimal point and bring down zeros.
3. **Add Decimal Point and 0s**:
- Write a decimal point in the quotient and add \( 0 \)s to the dividend (i.e., consider \( 3.000000 \)). Now looking at \( 30 \).
```
0.1__________
16 | 3.000000
```
4. **Divide 30 by 16**:
- \( 16 \) goes into \( 30 \) \( 1 \) time. Write \( 1 \) in the quotient.
- Multiply \( 1 \) by \( 16 \) and write \( 16 \) below \( 30 \).
```
0.1__________
16 | 3.000000
-16
________
14
```
5. **Bring Down the Next 0**:
- Bring down the next \( 0 \), making the new dividend \( 140 \).
```
0.1__________
16 | 3.000000
-16
________
140
```
6. **Divide 140 by 16**:
- \( 16 \) goes into \( 140 \) \( 8 \) times. Write \( 8 \) in the quotient.
- Multiply \( 8 \) by \( 16 \) getting \( 128 \) and write it below \( 140 \).
```
0.18_______
16 | 3.000000
-16
________
140
-128
________
12
```
7. **Bring Down Another 0**:
- Bring down another \( 0 \), making the new dividend \( 120 \).
```
0.18________
16 | 3.000000
-16
________
140
-128
________
120
```
8. **Divide 120 by 16**:
- \( 16 \) goes into \( 120 \) \( 7 \) times. Write \( 7 \) in the quotient.
- Multiply \( 7 \) by \( 16 \) getting \( 112 \) and write it below \( 120 \).
```
0.187______
16 | 3.000000
-16
________
140
-128
________
120
-112
________
8
```
9. **Bring Down Another 0**:
- Bring down another \( 0 \), making the new dividend \( 80 \).
```
0.187______
16 | 3.000000
-16
________
140
-128
________
120
-112
________
80
```
10. **Divide 80 by 16**:
- \( 16 \) goes into \( 80 \) \( 5 \) times. Write \( 5 \) in the quotient.
- Multiply \( 5 \) by \( 16 \) getting \( 80 \) and write it below \( 80 \).
```
0.1875____
16 | 3.000000
-16
________
140
-128
________
120
-112
________
80
-80
________
0
```
The remainder becomes \( 0 \), meaning the division is complete.
### Final Result:
From the long division, we find that
\[
\frac{3}{16} = 0.1875
\]
So the decimal representation of \( \frac{3}{16} \) is \( 0.1875 \). Thank you for your patience, and let me know if you need further assistance!
### Long Division of \( 3 \div 16 \):
1. **Set Up the Division**: Write \( 3 \) as the dividend and \( 16 \) as the divisor.
```
______________
16 | 3.000000
```
2. **Determine How Many Times 16 Goes into 3**:
- \( 16 \) goes into \( 3 \) \( 0 \) times, so we write \( 0 \) in the quotient. Since we need decimal division, we add a decimal point and bring down zeros.
3. **Add Decimal Point and 0s**:
- Write a decimal point in the quotient and add \( 0 \)s to the dividend (i.e., consider \( 3.000000 \)). Now looking at \( 30 \).
```
0.1__________
16 | 3.000000
```
4. **Divide 30 by 16**:
- \( 16 \) goes into \( 30 \) \( 1 \) time. Write \( 1 \) in the quotient.
- Multiply \( 1 \) by \( 16 \) and write \( 16 \) below \( 30 \).
```
0.1__________
16 | 3.000000
-16
________
14
```
5. **Bring Down the Next 0**:
- Bring down the next \( 0 \), making the new dividend \( 140 \).
```
0.1__________
16 | 3.000000
-16
________
140
```
6. **Divide 140 by 16**:
- \( 16 \) goes into \( 140 \) \( 8 \) times. Write \( 8 \) in the quotient.
- Multiply \( 8 \) by \( 16 \) getting \( 128 \) and write it below \( 140 \).
```
0.18_______
16 | 3.000000
-16
________
140
-128
________
12
```
7. **Bring Down Another 0**:
- Bring down another \( 0 \), making the new dividend \( 120 \).
```
0.18________
16 | 3.000000
-16
________
140
-128
________
120
```
8. **Divide 120 by 16**:
- \( 16 \) goes into \( 120 \) \( 7 \) times. Write \( 7 \) in the quotient.
- Multiply \( 7 \) by \( 16 \) getting \( 112 \) and write it below \( 120 \).
```
0.187______
16 | 3.000000
-16
________
140
-128
________
120
-112
________
8
```
9. **Bring Down Another 0**:
- Bring down another \( 0 \), making the new dividend \( 80 \).
```
0.187______
16 | 3.000000
-16
________
140
-128
________
120
-112
________
80
```
10. **Divide 80 by 16**:
- \( 16 \) goes into \( 80 \) \( 5 \) times. Write \( 5 \) in the quotient.
- Multiply \( 5 \) by \( 16 \) getting \( 80 \) and write it below \( 80 \).
```
0.1875____
16 | 3.000000
-16
________
140
-128
________
120
-112
________
80
-80
________
0
```
The remainder becomes \( 0 \), meaning the division is complete.
### Final Result:
From the long division, we find that
\[
\frac{3}{16} = 0.1875
\]
So the decimal representation of \( \frac{3}{16} \) is \( 0.1875 \). Thank you for your patience, and let me know if you need further assistance!