Let's divide 102659 by 38
We're looking to find how many times 38 goes into 102659.

On to step 1:
1 divided by 38 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 38

Advancing to step 2:
38 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Include the next digit (2) from the dividend after 10, then repeat: 102 / 38

Step 3:
102 divided by 38 is 2 with a remainder of 26.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 76 from 102 and we're left with 26.
Take the next digit (6) from the dividend and append it to 26, then repeat: 266 / 38

Advancing to step 4:
38 goes into 266 7 times with a remainder of 0.
Put 7 as the next digit of the answer. 
Result so far: 27.0
Subtract 266 from 266 to get 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 38

Let's proceed to step 5:
When dividing 5 by 38, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 270.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 38

Moving on to step 6:
38 goes into 59 1 times with a remainder of 21.
Put 1 as the next digit of the answer. 
Result so far: 2701.0
Subtract 38 from 59 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 7:
The number 38 fits into 210 5 times, leaving a remainder of 20.
Write down 5 as next digit of the result. 
Result so far: 2701.5
If we subtract 190 from 210, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
If we divide 200 by 38, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 2701.55
The remainder is 10 after subtracting 190 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Our division results in 2701.55 with a remaining 0.01.