971861 ÷ 95 
Our goal is to divide 971861 by 95.

On to step 1:
9 divided by 95 is 0 with a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Fetch the next digit (7) from the dividend, attach it to 9 and continue: 97 / 95

Moving on to step 2:
When dividing 97 by 95, we get 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
If we take 95 away from 97, we end up with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 95

Moving on to step 3:
The number 95 fits into 21 0 times, leaving a remainder of 21.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 21 and we're left with 21.
Fetch the next digit (8) from the dividend, attach it to 21 and continue: 218 / 95

On to step 4:
95 can be fit into 218 2 times, resulting in a remainder of 28.
The next digit of our result is 2. 
Result so far: 102.0
Deduct 190 from 218 and we're left with 28.
Take the next digit (6) from the dividend and append it to 28, then repeat: 286 / 95

Going ahead to step 5:
95 can be fit into 286 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 1023.0
The remainder is 1 after subtracting 285 from 286.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 95

On to step 6:
95 can be fit into 11 0 times, resulting in a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 10230.0
If we subtract 0 from 11, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
If we divide 110 by 95, we get 1 and a remainder of 15.
Write down 1 as next digit of the result. 
Result so far: 10230.1
Deduct 95 from 110 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
If we divide 150 by 95, we get 1 and a remainder of 55.
Use 1 as the next digit of our solution. 
Result so far: 10230.11
Deduct 95 from 150 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

In conclusion, the division gives 10230.11 with a balance of 0.055.