We're dividing 114129 by 66 
We're looking to find how many times 66 goes into 114129.

Let's proceed to step 1:
1 divided by 66 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 66

Advancing to step 2:
The number 66 fits into 11 0 times, leaving a remainder of 11.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 11 to get 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 66

Moving on to step 3:
66 goes into 114 1 times with a remainder of 48.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 66 from 114 leaves us with 48.
Grab the next digit (1) from the dividend, add it to 48, then carry on: 481 / 66

Advancing to step 4:
If we divide 481 by 66, we get 7 and a remainder of 19.
Use 7 as the next digit of our solution. 
Result so far: 17.0
The remainder is 19 after subtracting 462 from 481.
Append the next digit (2) from the dividend to 19 and continue with: 192 / 66

On to step 5:
66 can be fit into 192 2 times, resulting in a remainder of 60.
Record the quotient 2 as the next digit in the result. 
Result so far: 172.0
If we take 132 away from 192, we end up with 60.
Grab the next digit (9) from the dividend, add it to 60, then carry on: 609 / 66

Advancing to step 6:
66 goes into 609 9 times with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 1729.0
Deduct 594 from 609 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.

Moving on to step 7:
The number 66 fits into 150 2 times, leaving a remainder of 18.
The next digit of our result is 2. 
Result so far: 1729.2
The remainder is 18 after subtracting 132 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 8:
66 goes into 180 2 times with a remainder of 48.
Use 2 as the next digit of our solution. 
Result so far: 1729.22
If we take 132 away from 180, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

In conclusion, the division gives 1729.22 with a balance of 0.048.