109259 ÷ 91 
Our goal is to divide 109259 by 91.

Let's proceed to step 1:
91 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 91

Step 2:
When dividing 10 by 91, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (9) from the dividend, attach it to 10 and continue: 109 / 91

Advancing to step 3:
109 divided by 91 is 1 with a remainder of 18.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 91 from 109 to get 18.
Take the next digit (2) from the dividend and append it to 18, then repeat: 182 / 91

Moving on to step 4:
182 divided by 91 is 2 with a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 12.0
Subtracting 182 from 182 leaves us with 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 91

Going ahead to step 5:
If we divide 5 by 91, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 120.0
If we subtract 0 from 5, we get 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 91

On to step 6:
59 divided by 91 is 0 with a remainder of 59.
Record the quotient 0 as the next digit in the result. 
Result so far: 1200.0
If we take 0 away from 59, we end up with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Let's proceed to step 7:
When dividing 590 by 91, we get 6 with a remainder of 44.
Record the quotient 6 as the next digit in the result. 
Result so far: 1200.6
If we subtract 546 from 590, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 8:
91 can be fit into 440 4 times, resulting in a remainder of 76.
The next digit of our result is 4. 
Result so far: 1200.64
If we subtract 364 from 440, we get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 9:
The number 91 fits into 760 8 times, leaving a remainder of 32.
Write down 8 as next digit of the result. 
Result so far: 1200.648
The remainder is 32 after subtracting 728 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Going ahead to step 10:
If we divide 320 by 91, we get 3 and a remainder of 47.
Write down 3 as next digit of the result. 
Result so far: 1200.6483
If we subtract 273 from 320, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Moving on to step 11:
91 can be fit into 470 5 times, resulting in a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 1200.64835
The remainder is 15 after subtracting 455 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 12:
91 goes into 150 1 times with a remainder of 59.
Use 1 as the next digit of our solution. 
Result so far: 1200.648351
Deduct 91 from 150 and we're left with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 13:
The number 91 fits into 590 6 times, leaving a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 1200.6483516
Subtract 546 from 590 to get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 14:
If we divide 440 by 91, we get 4 and a remainder of 76.
Write down 4 as next digit of the result. 
Result so far: 1200.64835164
If we take 364 away from 440, we end up with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

After the division, we end up with 1200.64835164 and a remainder of 7.6e-08.