91114 ÷ 89 
Our goal is to divide 91114 by 89.

On to step 1:
89 can be fit into 9 0 times, resulting in a remainder of 9.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Take the next digit (1) from the dividend and append it to 9, then repeat: 91 / 89

Step 2:
89 can be fit into 91 1 times, resulting in a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 89 away from 91, we end up with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 89

Step 3:
89 can be fit into 21 0 times, resulting in a remainder of 21.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Subtract 0 from 21 to get 21.
Take the next digit (1) from the dividend and append it to 21, then repeat: 211 / 89

Moving on to step 4:
If we divide 211 by 89, we get 2 and a remainder of 33.
Write down 2 as next digit of the result. 
Result so far: 102.0
If we take 178 away from 211, we end up with 33.
Append the next digit (4) from the dividend to 33 and continue with: 334 / 89

Advancing to step 5:
334 divided by 89 is 3 with a remainder of 67.
The next digit of our result is 3. 
Result so far: 1023.0
Subtracting 267 from 334 leaves us with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 6:
If we divide 670 by 89, we get 7 and a remainder of 47.
Write down 7 as next digit of the result. 
Result so far: 1023.7
Subtract 623 from 670 to 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.

Going ahead to step 7:
The number 89 fits into 470 5 times, leaving a remainder of 25.
The next digit of our result is 5. 
Result so far: 1023.75
Subtracting 445 from 470 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
89 can be fit into 250 2 times, resulting in a remainder of 72.
Use 2 as the next digit of our solution. 
Result so far: 1023.752
If we take 178 away from 250, we end up with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Moving on to step 9:
89 goes into 720 8 times with a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 1023.7528
The remainder is 8 after subtracting 712 from 720.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
89 can be fit into 80 0 times, resulting in a remainder of 80.
Put 0 as the next digit of the answer. 
Result so far: 1023.7528
If we take 0 away from 80, we end up with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Advancing to step 11:
89 goes into 800 8 times with a remainder of 88.
Use 8 as the next digit of our solution. 
Result so far: 1023.752808
Deduct 712 from 800 and we're left with 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Step 12:
89 can be fit into 880 9 times, resulting in a remainder of 79.
Record the quotient 9 as the next digit in the result. 
Result so far: 1023.7528089
If we subtract 801 from 880, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

On to step 13:
The number 89 fits into 790 8 times, leaving a remainder of 78.
The next digit of our result is 8. 
Result so far: 1023.75280898
Deduct 712 from 790 and we're left with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

The final result is 1023.75280898 with a remainder of 7.8e-08.