41008101 ÷ 97 
We want to figure out the number of times 41008101 can be divided by 97.

Moving on to step 1:
If we divide 4 by 97, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 97

On to step 2:
41 divided by 97 is 0 with a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 41 after subtracting 0 from 41.
Take the next digit (0) from the dividend and append it to 41, then repeat: 410 / 97

Let's proceed to step 3:
When dividing 410 by 97, we get 4 with a remainder of 22.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Deduct 388 from 410 and we're left with 22.
Take the next digit (0) from the dividend and append it to 22, then repeat: 220 / 97

Going ahead to step 4:
If we divide 220 by 97, we get 2 and a remainder of 26.
Write down 2 as next digit of the result. 
Result so far: 42.0
The remainder is 26 after subtracting 194 from 220.
Take the next digit (8) from the dividend and append it to 26, then repeat: 268 / 97

Going ahead to step 5:
When dividing 268 by 97, we get 2 with a remainder of 74.
Use 2 as the next digit of our solution. 
Result so far: 422.0
If we subtract 194 from 268, we get 74.
Grab the next digit (1) from the dividend, add it to 74, then carry on: 741 / 97

On to step 6:
97 goes into 741 7 times with a remainder of 62.
Use 7 as the next digit of our solution. 
Result so far: 4227.0
The remainder is 62 after subtracting 679 from 741.
Include the next digit (0) from the dividend after 62, then repeat: 620 / 97

Moving on to step 7:
620 divided by 97 is 6 with a remainder of 38.
The number 6 becomes the next digit in our result. 
Result so far: 42276.0
If we take 582 away from 620, we end up with 38.
Include the next digit (1) from the dividend after 38, then repeat: 381 / 97

On to step 8:
When dividing 381 by 97, we get 3 with a remainder of 90.
Put 3 as the next digit of the answer. 
Result so far: 422763.0
The remainder is 90 after subtracting 291 from 381.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Going ahead to step 9:
If we divide 900 by 97, we get 9 and a remainder of 27.
Use 9 as the next digit of our solution. 
Result so far: 422763.9
The remainder is 27 after subtracting 873 from 900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 10:
97 can be fit into 270 2 times, resulting in a remainder of 76.
The number 2 becomes the next digit in our result. 
Result so far: 422763.92
Deduct 194 from 270 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 11:
If we divide 760 by 97, we get 7 and a remainder of 81.
The next digit of our result is 7. 
Result so far: 422763.927
Deduct 679 from 760 and we're left with 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Going ahead to step 12:
810 divided by 97 is 8 with a remainder of 34.
The next digit of our result is 8. 
Result so far: 422763.9278
If we take 776 away from 810, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 13:
97 can be fit into 340 3 times, resulting in a remainder of 49.
Write down 3 as next digit of the result. 
Result so far: 422763.92783
Subtract 291 from 340 to get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

On to step 14:
When dividing 490 by 97, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 422763.927835
If we subtract 485 from 490, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 15:
97 can be fit into 50 0 times, resulting in a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 422763.927835
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 16:
97 can be fit into 500 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 422763.92783505
Deduct 485 from 500 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.

The final outcome is 422763.92783505, with a leftover of 1.5e-08.