101093 ÷ 11 
We're looking to find how many times 11 goes into 101093.

Let's proceed to step 1:
If we divide 1 by 11, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 11

Moving on to step 2:
When dividing 10 by 11, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 11

Going ahead to step 3:
When dividing 101 by 11, we get 9 with a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtracting 99 from 101 leaves us with 2.
Take the next digit (0) from the dividend and append it to 2, then repeat: 20 / 11

Moving on to step 4:
The number 11 fits into 20 1 times, leaving a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 91.0
The remainder is 9 after subtracting 11 from 20.
Take the next digit (9) from the dividend and append it to 9, then repeat: 99 / 11

On to step 5:
99 divided by 11 is 9 with a remainder of 0.
Write down 9 as next digit of the result. 
Result so far: 919.0
Subtract 99 from 99 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 11

Advancing to step 6:
3 divided by 11 is 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 9190.0
The remainder is 3 after subtracting 0 from 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
11 goes into 30 2 times with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 9190.2
Deduct 22 from 30 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
When dividing 80 by 11, we get 7 with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 9190.27
The remainder is 3 after subtracting 77 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 9:
30 divided by 11 is 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 9190.272
The remainder is 8 after subtracting 22 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 10:
80 divided by 11 is 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 9190.2727
Subtract 77 from 80 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 11:
If we divide 30 by 11, we get 2 and a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 9190.27272
If we subtract 22 from 30, we get 8.
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 12:
80 divided by 11 is 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 9190.272727
If we subtract 77 from 80, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 13:
If we divide 30 by 11, we get 2 and a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 9190.2727272
The remainder is 8 after subtracting 22 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 14:
When dividing 80 by 11, we get 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 9190.27272727
If we take 77 away from 80, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 9190.27272727 and a remainder of 3e-09.