We look at the division of 510332 by 45 
We want to divide 510332 by 45.

Let's proceed to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 45

On to step 2:
When dividing 51 by 45, we get 1 with a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 45 from 51 and we're left with 6.
Include the next digit (0) from the dividend after 6, then repeat: 60 / 45

Step 3:
45 goes into 60 1 times with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Subtracting 45 from 60 leaves us with 15.
Take the next digit (3) from the dividend and append it to 15, then repeat: 153 / 45

Step 4:
153 divided by 45 is 3 with a remainder of 18.
The next digit of our result is 3. 
Result so far: 113.0
If we subtract 135 from 153, we get 18.
Fetch the next digit (3) from the dividend, attach it to 18 and continue: 183 / 45

Advancing to step 5:
When dividing 183 by 45, we get 4 with a remainder of 3.
Use 4 as the next digit of our solution. 
Result so far: 1134.0
Subtract 180 from 183 to get 3.
Grab the next digit (2) from the dividend, add it to 3, then carry on: 32 / 45

Let's proceed to step 6:
45 can be fit into 32 0 times, resulting in a remainder of 32.
The next digit of our result is 0. 
Result so far: 11340.0
If we take 0 away from 32, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
If we divide 320 by 45, we get 7 and a remainder of 5.
The next digit of our result is 7. 
Result so far: 11340.7
Subtracting 315 from 320 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
If we divide 50 by 45, we get 1 and a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 11340.71
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 9:
If we divide 50 by 45, we get 1 and a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 11340.711
Subtracting 45 from 50 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 11340.711, and the remainder is 0.0005.