We look at the division of 105181 by 71 
We're looking to find how many times 71 goes into 105181.

Advancing to step 1:
71 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 71

Going ahead to step 2:
10 divided by 71 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 71

On to step 3:
71 goes into 105 1 times with a remainder of 34.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 71 from 105, we get 34.
Take the next digit (1) from the dividend and append it to 34, then repeat: 341 / 71

Advancing to step 4:
If we divide 341 by 71, we get 4 and a remainder of 57.
The next digit of our result is 4. 
Result so far: 14.0
Deduct 284 from 341 and we're left with 57.
Grab the next digit (8) from the dividend, add it to 57, then carry on: 578 / 71

Going ahead to step 5:
When dividing 578 by 71, we get 8 with a remainder of 10.
The next digit of our result is 8. 
Result so far: 148.0
Subtracting 568 from 578 leaves us with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 71

Advancing to step 6:
101 divided by 71 is 1 with a remainder of 30.
The number 1 becomes the next digit in our result. 
Result so far: 1481.0
The remainder is 30 after subtracting 71 from 101.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
300 divided by 71 is 4 with a remainder of 16.
Put 4 as the next digit of the answer. 
Result so far: 1481.4
Subtract 284 from 300 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 8:
160 divided by 71 is 2 with a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 1481.42
Deduct 142 from 160 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 9:
When dividing 180 by 71, we get 2 with a remainder of 38.
The next digit of our result is 2. 
Result so far: 1481.422
Subtract 142 from 180 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

In conclusion, the division gives 1481.422 with a balance of 0.0038.