4082 ÷ 97 
We want to figure out the number of times 4082 can be divided by 97.

Step 1:
97 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Grab the next digit (0) from the dividend, add it to 4, then carry on: 40 / 97

Moving on to step 2:
When dividing 40 by 97, we get 0 with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 40 to get 40.
Append the next digit (8) from the dividend to 40 and continue with: 408 / 97

Going ahead to step 3:
97 can be fit into 408 4 times, resulting in a remainder of 20.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtract 388 from 408 to get 20.
Bring next digit (2) of the dividend behind the 20 and repeat the process: 202 / 97

Advancing to step 4:
If we divide 202 by 97, we get 2 and a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 42.0
Subtract 194 from 202 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 5:
The number 97 fits into 80 0 times, leaving a remainder of 80.
The next digit of our result is 0. 
Result so far: 42.0
If we subtract 0 from 80, we get 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Going ahead to step 6:
97 can be fit into 800 8 times, resulting in a remainder of 24.
The next digit of our result is 8. 
Result so far: 42.08
Subtract 776 from 800 to 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.

Going ahead to step 7:
97 can be fit into 240 2 times, resulting in a remainder of 46.
The next digit of our result is 2. 
Result so far: 42.082
If we take 194 away from 240, we end up 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.

Moving on to step 8:
460 divided by 97 is 4 with a remainder of 72.
Record the quotient 4 as the next digit in the result. 
Result so far: 42.0824
If we take 388 away from 460, we end up with 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 9:
720 divided by 97 is 7 with a remainder of 41.
Write down 7 as next digit of the result. 
Result so far: 42.08247
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.

On to step 10:
97 goes into 410 4 times with a remainder of 22.
The number 4 becomes the next digit in our result. 
Result so far: 42.082474
Subtract 388 from 410 to get 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 11:
97 goes into 220 2 times with a remainder of 26.
Use 2 as the next digit of our solution. 
Result so far: 42.0824742
Subtracting 194 from 220 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 12:
If we divide 260 by 97, we get 2 and a remainder of 66.
The number 2 becomes the next digit in our result. 
Result so far: 42.08247422
Subtracting 194 from 260 leaves us with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Our division results in 42.08247422 with a remaining 6.6e-08.