1271121 ÷ 127 
Our goal is to divide 1271121 by 127.

Going ahead to step 1:
If we divide 1 by 127, we get 0 and 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.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 127

Advancing to step 2:
When dividing 12 by 127, we get 0 with a remainder of 12.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 127

Advancing to step 3:
127 divided by 127 is 1 with a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 127 from 127 to get 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 127

Let's proceed to step 4:
1 divided by 127 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we take 0 away from 1, we end up with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 127

Going ahead to step 5:
The number 127 fits into 11 0 times, leaving a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 100.0
Subtracting 0 from 11 leaves us with 11.
Fetch the next digit (2) from the dividend, attach it to 11 and continue: 112 / 127

Going ahead to step 6:
When dividing 112 by 127, we get 0 with a remainder of 112.
The next digit of our result is 0. 
Result so far: 1000.0
Deduct 0 from 112 and we're left with 112.
Include the next digit (1) from the dividend after 112, then repeat: 1121 / 127

Going ahead to step 7:
127 can be fit into 1121 8 times, resulting in a remainder of 105.
Write down 8 as next digit of the result. 
Result so far: 10008.0
The remainder is 105 after subtracting 1016 from 1121.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1050, and continue the process.

Going ahead to step 8:
If we divide 1050 by 127, we get 8 and a remainder of 34.
Use 8 as the next digit of our solution. 
Result so far: 10008.8
If we subtract 1016 from 1050, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 9:
340 divided by 127 is 2 with a remainder of 86.
Record the quotient 2 as the next digit in the result. 
Result so far: 10008.82
Deduct 254 from 340 and we're left with 86.
Since there are no more digits in the dividend, we add a zero to the remainder making it 860, and continue the process.

On to step 10:
127 can be fit into 860 6 times, resulting in a remainder of 98.
The number 6 becomes the next digit in our result. 
Result so far: 10008.826
Deduct 762 from 860 and we're left with 98.
Since there are no more digits in the dividend, we add a zero to the remainder making it 980, and continue the process.

Let's proceed to step 11:
127 can be fit into 980 7 times, resulting in a remainder of 91.
Write down 7 as next digit of the result. 
Result so far: 10008.8267
Subtract 889 from 980 to get 91.
Since there are no more digits in the dividend, we add a zero to the remainder making it 910, and continue the process.

Step 12:
If we divide 910 by 127, we get 7 and a remainder of 21.
Use 7 as the next digit of our solution. 
Result so far: 10008.82677
Subtracting 889 from 910 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

The final result is 10008.82677 with a remainder of 2.1e-05.