We're dividing 659 by 61 
We're looking to find how many times 61 goes into 659.

Going ahead to step 1:
The number 61 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (5) from the dividend after 6, then repeat: 65 / 61

Going ahead to step 2:
65 divided by 61 is 1 with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 61 from 65, we get 4.
Append the next digit (9) from the dividend to 4 and continue with: 49 / 61

Let's proceed to step 3:
If we divide 49 by 61, we get 0 and a remainder of 49.
The next digit of our result is 0. 
Result so far: 10.0
Subtracting 0 from 49 leaves us with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Let's proceed to step 4:
61 goes into 490 8 times with a remainder of 2.
The next digit of our result is 8. 
Result so far: 10.8
Deduct 488 from 490 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 5:
If we divide 20 by 61, we get 0 and a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 10.8
Subtracting 0 from 20 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 6:
61 can be fit into 200 3 times, resulting in a remainder of 17.
Put 3 as the next digit of the answer. 
Result so far: 10.803
Subtracting 183 from 200 leaves us with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 7:
61 can be fit into 170 2 times, resulting in a remainder of 48.
Use 2 as the next digit of our solution. 
Result so far: 10.8032
If we subtract 122 from 170, we get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 8:
61 goes into 480 7 times with a remainder of 53.
The next digit of our result is 7. 
Result so far: 10.80327
If we subtract 427 from 480, we get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Let's proceed to step 9:
When dividing 530 by 61, we get 8 with a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 10.803278
Subtracting 488 from 530 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 10:
61 goes into 420 6 times with a remainder of 54.
The number 6 becomes the next digit in our result. 
Result so far: 10.8032786
Subtracting 366 from 420 leaves us with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 11:
540 divided by 61 is 8 with a remainder of 52.
The next digit of our result is 8. 
Result so far: 10.80327868
Subtracting 488 from 540 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

After the division, we end up with 10.80327868 and a remainder of 5.2e-08.