We look at the division of 4503 by 34 
We want to figure out the number of times 4503 can be divided by 34.

Step 1:
If we divide 4 by 34, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Fetch the next digit (5) from the dividend, attach it to 4 and continue: 45 / 34

Let's proceed to step 2:
When dividing 45 by 34, we get 1 with a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 34 from 45 and we're left with 11.
Bring next digit (0) of the dividend behind the 11 and repeat the process: 110 / 34

Let's proceed to step 3:
The number 34 fits into 110 3 times, leaving a remainder of 8.
The next digit of our result is 3. 
Result so far: 13.0
Subtract 102 from 110 to get 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 34

Going ahead to step 4:
83 divided by 34 is 2 with a remainder of 15.
The next digit of our result is 2. 
Result so far: 132.0
Deduct 68 from 83 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.

Going ahead to step 5:
150 divided by 34 is 4 with a remainder of 14.
The next digit of our result is 4. 
Result so far: 132.4
Deduct 136 from 150 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 6:
If we divide 140 by 34, we get 4 and a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 132.44
If we take 136 away from 140, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 132.44, with a leftover of 0.004.