We look at the division of 35942929 by 503 
We're looking to find how many times 503 goes into 35942929.

Advancing to step 1:
If we divide 3 by 503, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 503

Step 2:
503 can be fit into 35 0 times, resulting in a remainder of 35.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 35 after subtracting 0 from 35.
Include the next digit (9) from the dividend after 35, then repeat: 359 / 503

Going ahead to step 3:
If we divide 359 by 503, we get 0 and a remainder of 359.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 359 and we're left with 359.
Append the next digit (4) from the dividend to 359 and continue with: 3594 / 503

Step 4:
3594 divided by 503 is 7 with a remainder of 73.
The next digit of our result is 7. 
Result so far: 7.0
Deduct 3521 from 3594 and we're left with 73.
Fetch the next digit (2) from the dividend, attach it to 73 and continue: 732 / 503

Going ahead to step 5:
732 divided by 503 is 1 with a remainder of 229.
The number 1 becomes the next digit in our result. 
Result so far: 71.0
Subtracting 503 from 732 leaves us with 229.
Include the next digit (9) from the dividend after 229, then repeat: 2299 / 503

Moving on to step 6:
2299 divided by 503 is 4 with a remainder of 287.
Put 4 as the next digit of the answer. 
Result so far: 714.0
Deduct 2012 from 2299 and we're left with 287.
Fetch the next digit (2) from the dividend, attach it to 287 and continue: 2872 / 503

Going ahead to step 7:
The number 503 fits into 2872 5 times, leaving a remainder of 357.
Use 5 as the next digit of our solution. 
Result so far: 7145.0
If we subtract 2515 from 2872, we get 357.
Fetch the next digit (9) from the dividend, attach it to 357 and continue: 3579 / 503

Let's proceed to step 8:
When dividing 3579 by 503, we get 7 with a remainder of 58.
Use 7 as the next digit of our solution. 
Result so far: 71457.0
If we take 3521 away from 3579, we end up with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 9:
When dividing 580 by 503, we get 1 with a remainder of 77.
Put 1 as the next digit of the answer. 
Result so far: 71457.1
Deduct 503 from 580 and we're left with 77.
Since there are no more digits in the dividend, we add a zero to the remainder making it 770, and continue the process.

On to step 10:
The number 503 fits into 770 1 times, leaving a remainder of 267.
Use 1 as the next digit of our solution. 
Result so far: 71457.11
Subtracting 503 from 770 leaves us with 267.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2670, and continue the process.

In conclusion, the division gives 71457.11 with a balance of 0.267.