Let's divide 510910 by 45
We want to figure out the number of times 510910 can be divided by 45.

Step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 45

On to step 2:
The number 45 fits into 51 1 times, leaving a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 45 away from 51, we end up with 6.
Take the next digit (0) from the dividend and append it to 6, then repeat: 60 / 45

Step 3:
When dividing 60 by 45, we get 1 with a remainder of 15.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we take 45 away from 60, we end up with 15.
Grab the next digit (9) from the dividend, add it to 15, then carry on: 159 / 45

On to step 4:
45 goes into 159 3 times with a remainder of 24.
The number 3 becomes the next digit in our result. 
Result so far: 113.0
If we subtract 135 from 159, we get 24.
Bring next digit (1) of the dividend behind the 24 and repeat the process: 241 / 45

Step 5:
If we divide 241 by 45, we get 5 and a remainder of 16.
Record the quotient 5 as the next digit in the result. 
Result so far: 1135.0
Deduct 225 from 241 and we're left with 16.
Include the next digit (0) from the dividend after 16, then repeat: 160 / 45

Step 6:
The number 45 fits into 160 3 times, leaving a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 11353.0
If we take 135 away from 160, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 7:
When dividing 250 by 45, we get 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 11353.5
If we take 225 away from 250, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
45 goes into 250 5 times with a remainder of 25.
The next digit of our result is 5. 
Result so far: 11353.55
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 11353.55 with a balance of 0.025.