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Sagot :
To divide 100 by 6.5, we will follow the standard method of long division.
Step-by-Step Solution:
1. Setup the Division:
```
6.5 | 100.0
```
2. Adjust to Whole Numbers:
Since we have a decimal in the divisor (6.5), we can multiply both the dividend and the divisor by 10 to make the divisor a whole number.
This changes the problem to:
```
65 | 1000.0
```
3. Perform the Division:
- First digit:
- 65 goes into 100 one time.
- Write 1 above the line.
- Multiply 1 by 65, which gives 65.
- Subtract 65 from 100, which leaves 35.
```
1
65 | 1000.0
-65
-----
350
```
- Next digit:
- Bring down the next 0 to make it 350.
- 65 goes into 350 five times.
- Write 5 next to the 1.
- Multiply 5 by 65, which gives 325.
- Subtract 325 from 350, which leaves 25.
```
15
65 | 1000.0
- 65
-----
350
-325
-----
250
```
- Next digit:
- Bring down the next 0 to make it 250.
- 65 goes into 250 three times.
- Write 3 next to the 15.
- Multiply 3 by 65, which gives 195.
- Subtract 195 from 250, which leaves 55.
```
15.3
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
```
- Next digit:
- Bring down the next 0 to make it 550.
- 65 goes into 550 eight times.
- Write 8 next to the 15.3.
- Multiply 8 by 65, which gives 520.
- Subtract 520 from 550, which leaves 30.
```
15.38
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
- 520
-----
30
```
- Next digit:
- Bring down the next 0 to make it 300.
- 65 goes into 300 four times.
- Write 4 next to the 15.38.
- Multiply 4 by 65, which gives 260.
- Subtract 260 from 300, which leaves 40.
```
15.384
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
-520
-----
300
-260
----
40
```
- Next digit:
- Bring down the final 0 to make it 400.
- 65 goes into 400 six times.
- Write 6 next to the 15.384.
- Multiply 6 by 65, which gives 390.
- Subtract 390 from 400, which leaves 10.
```
15.3846
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
-520
-----
300
-260
----
40
-390
------
10
```
4. Terminating:
You could repeat the division process however we notice the answer begins to closely approach our solution of 15.3846. So approximating at the fourth decimal:
The quotient is:
[tex]\[ 15.384615384615385 \][/tex]
Thus, 100 divided by 6.5 yields approximately 15.3846 when rounded to four decimal places.
Step-by-Step Solution:
1. Setup the Division:
```
6.5 | 100.0
```
2. Adjust to Whole Numbers:
Since we have a decimal in the divisor (6.5), we can multiply both the dividend and the divisor by 10 to make the divisor a whole number.
This changes the problem to:
```
65 | 1000.0
```
3. Perform the Division:
- First digit:
- 65 goes into 100 one time.
- Write 1 above the line.
- Multiply 1 by 65, which gives 65.
- Subtract 65 from 100, which leaves 35.
```
1
65 | 1000.0
-65
-----
350
```
- Next digit:
- Bring down the next 0 to make it 350.
- 65 goes into 350 five times.
- Write 5 next to the 1.
- Multiply 5 by 65, which gives 325.
- Subtract 325 from 350, which leaves 25.
```
15
65 | 1000.0
- 65
-----
350
-325
-----
250
```
- Next digit:
- Bring down the next 0 to make it 250.
- 65 goes into 250 three times.
- Write 3 next to the 15.
- Multiply 3 by 65, which gives 195.
- Subtract 195 from 250, which leaves 55.
```
15.3
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
```
- Next digit:
- Bring down the next 0 to make it 550.
- 65 goes into 550 eight times.
- Write 8 next to the 15.3.
- Multiply 8 by 65, which gives 520.
- Subtract 520 from 550, which leaves 30.
```
15.38
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
- 520
-----
30
```
- Next digit:
- Bring down the next 0 to make it 300.
- 65 goes into 300 four times.
- Write 4 next to the 15.38.
- Multiply 4 by 65, which gives 260.
- Subtract 260 from 300, which leaves 40.
```
15.384
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
-520
-----
300
-260
----
40
```
- Next digit:
- Bring down the final 0 to make it 400.
- 65 goes into 400 six times.
- Write 6 next to the 15.384.
- Multiply 6 by 65, which gives 390.
- Subtract 390 from 400, which leaves 10.
```
15.3846
65 | 1000.0
- 65
-----
350
-325
-----
250
-195
-----
55
-520
-----
300
-260
----
40
-390
------
10
```
4. Terminating:
You could repeat the division process however we notice the answer begins to closely approach our solution of 15.3846. So approximating at the fourth decimal:
The quotient is:
[tex]\[ 15.384615384615385 \][/tex]
Thus, 100 divided by 6.5 yields approximately 15.3846 when rounded to four decimal places.
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