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Bot GPT 4-o mini To convert the fraction \( \frac{13}{20} \) to a decimal using long division, follow these steps:
1. **Set Up**: We want to divide 13 by 20. Since 13 is less than 20, we know that our decimal will start with 0.000. We'll actually be dividing 130 by adding a decimal point and a zero.
```
0.650
_________
20 | 13.000
- 0
```
2. **Divide**:
- 20 goes into 130 six times (because \( 20 \times 6 = 120 \)).
- Write the 6 above the division bar.
```
0.6
_________
20 | 13.000
- 120
-------
```
3. **Subtract**:
- Subtract 120 from 130, which gives us 10.
```
0.6
_________
20 | 13.000
- 120
-------
10
```
4. **Bring Down the Next Digit**:
- Bring down the next 0 (making it 100).
```
0.6
_________
20 | 13.000
- 120
-------
100
```
5. **Divide Again**:
- 20 goes into 100 five times (because \( 20 \times 5 = 100 \)).
- Write the 5 above the division bar next to the 6.
```
0.65
_________
20 | 13.000
- 120
-------
100
- 100
-------
0
```
6. **Subtract Again**:
- Subtract 100 from 100, which gives us 0.
At this point, there are no more numbers to bring down, and we reached a remainder of 0. Therefore, the division is complete.
Thus, \( \frac{13}{20} \) as a decimal is:
\[
0.65
\]