509521 ÷ 45 
Our goal is to divide 509521 by 45.

Step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 45

On to step 2:
When dividing 50 by 45, we get 1 with a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 45 from 50 to get 5.
Include the next digit (9) from the dividend after 5, then repeat: 59 / 45

Let's proceed to step 3:
If we divide 59 by 45, we get 1 and a remainder of 14.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
Deduct 45 from 59 and we're left with 14.
Append the next digit (5) from the dividend to 14 and continue with: 145 / 45

Moving on to step 4:
The number 45 fits into 145 3 times, leaving a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 113.0
If we subtract 135 from 145, we get 10.
Append the next digit (2) from the dividend to 10 and continue with: 102 / 45

Advancing to step 5:
If we divide 102 by 45, we get 2 and a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 1132.0
If we subtract 90 from 102, we get 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 45

On to step 6:
45 can be fit into 121 2 times, resulting in a remainder of 31.
The number 2 becomes the next digit in our result. 
Result so far: 11322.0
If we take 90 away from 121, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Moving on to step 7:
45 can be fit into 310 6 times, resulting in a remainder of 40.
Put 6 as the next digit of the answer. 
Result so far: 11322.6
If we take 270 away from 310, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 8:
The number 45 fits into 400 8 times, leaving a remainder of 40.
Write down 8 as next digit of the result. 
Result so far: 11322.68
Subtract 360 from 400 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 9:
When dividing 400 by 45, we get 8 with a remainder of 40.
Use 8 as the next digit of our solution. 
Result so far: 11322.688
Deduct 360 from 400 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

In conclusion, the division gives 11322.688 with a balance of 0.004.