We look at the division of 629125 by 84 
We want to figure out the number of times 629125 can be divided by 84.

Advancing to step 1:
84 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 84

Step 2:
84 goes into 62 0 times with a remainder of 62.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 62, we end up with 62.
Include the next digit (9) from the dividend after 62, then repeat: 629 / 84

On to step 3:
84 can be fit into 629 7 times, resulting in a remainder of 41.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtract 588 from 629 to get 41.
Take the next digit (1) from the dividend and append it to 41, then repeat: 411 / 84

Step 4:
411 divided by 84 is 4 with a remainder of 75.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
Subtracting 336 from 411 leaves us with 75.
Include the next digit (2) from the dividend after 75, then repeat: 752 / 84

Advancing to step 5:
752 divided by 84 is 8 with a remainder of 80.
Use 8 as the next digit of our solution. 
Result so far: 748.0
Deduct 672 from 752 and we're left with 80.
Append the next digit (5) from the dividend to 80 and continue with: 805 / 84

Step 6:
When dividing 805 by 84, we get 9 with a remainder of 49.
Record the quotient 9 as the next digit in the result. 
Result so far: 7489.0
The remainder is 49 after subtracting 756 from 805.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 7:
The number 84 fits into 490 5 times, leaving a remainder of 70.
The next digit of our result is 5. 
Result so far: 7489.5
If we subtract 420 from 490, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 8:
84 goes into 700 8 times with a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 7489.58
Subtract 672 from 700 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 9:
84 can be fit into 280 3 times, resulting in a remainder of 28.
Write down 3 as next digit of the result. 
Result so far: 7489.583
Subtract 252 from 280 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 10:
The number 84 fits into 280 3 times, leaving a remainder of 28.
The number 3 becomes the next digit in our result. 
Result so far: 7489.5833
Subtract 252 from 280 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

In conclusion, the division gives 7489.5833 with a balance of 0.00028.