We look at the division of 905166 by 97 
We're looking to find how many times 97 goes into 905166.

Step 1:
9 divided by 97 is 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Include the next digit (0) from the dividend after 9, then repeat: 90 / 97

Moving on to step 2:
97 can be fit into 90 0 times, resulting in a remainder of 90.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 90 to get 90.
Append the next digit (5) from the dividend to 90 and continue with: 905 / 97

Moving on to step 3:
If we divide 905 by 97, we get 9 and a remainder of 32.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
The remainder is 32 after subtracting 873 from 905.
Grab the next digit (1) from the dividend, add it to 32, then carry on: 321 / 97

On to step 4:
The number 97 fits into 321 3 times, leaving a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 93.0
Deduct 291 from 321 and we're left with 30.
Append the next digit (6) from the dividend to 30 and continue with: 306 / 97

Step 5:
306 divided by 97 is 3 with a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 933.0
Deduct 291 from 306 and we're left with 15.
Grab the next digit (6) from the dividend, add it to 15, then carry on: 156 / 97

Advancing to step 6:
97 can be fit into 156 1 times, resulting in a remainder of 59.
Put 1 as the next digit of the answer. 
Result so far: 9331.0
Subtract 97 from 156 to get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

On to step 7:
97 can be fit into 590 6 times, resulting in a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 9331.6
Subtract 582 from 590 to 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.

Let's proceed to step 8:
The number 97 fits into 80 0 times, leaving a remainder of 80.
Put 0 as the next digit of the answer. 
Result so far: 9331.6
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.

Step 9:
97 can be fit into 800 8 times, resulting in a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 9331.608
If we subtract 776 from 800, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 10:
If we divide 240 by 97, we get 2 and a remainder of 46.
The number 2 becomes the next digit in our result. 
Result so far: 9331.6082
Subtracting 194 from 240 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Advancing to step 11:
460 divided by 97 is 4 with a remainder of 72.
The number 4 becomes the next digit in our result. 
Result so far: 9331.60824
If we subtract 388 from 460, we get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

On to step 12:
When dividing 720 by 97, we get 7 with a remainder of 41.
Put 7 as the next digit of the answer. 
Result so far: 9331.608247
The remainder is 41 after subtracting 679 from 720.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Advancing to step 13:
97 can be fit into 410 4 times, resulting in a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 9331.6082474
Subtracting 388 from 410 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 14:
If we divide 220 by 97, we get 2 and a remainder of 26.
The number 2 becomes the next digit in our result. 
Result so far: 9331.60824742
Subtract 194 from 220 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

In conclusion, the division gives 9331.60824742 with a balance of 2.6e-08.