We look at the division of 509137 by 45 
Our goal is to divide 509137 by 45.

On to step 1:
45 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 45

Advancing to step 2:
If we divide 50 by 45, we get 1 and a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 5 after subtracting 45 from 50.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 45

On to step 3:
The number 45 fits into 59 1 times, leaving a remainder of 14.
Use 1 as the next digit of our solution. 
Result so far: 11.0
If we subtract 45 from 59, we get 14.
Grab the next digit (1) from the dividend, add it to 14, then carry on: 141 / 45

Moving on to step 4:
When dividing 141 by 45, we get 3 with a remainder of 6.
The next digit of our result is 3. 
Result so far: 113.0
Deduct 135 from 141 and we're left with 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 45

Moving on to step 5:
45 goes into 63 1 times with a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 1131.0
Subtracting 45 from 63 leaves us with 18.
Fetch the next digit (7) from the dividend, attach it to 18 and continue: 187 / 45

Moving on to step 6:
45 can be fit into 187 4 times, resulting in a remainder of 7.
Record the quotient 4 as the next digit in the result. 
Result so far: 11314.0
Subtracting 180 from 187 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
When dividing 70 by 45, we get 1 with a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 11314.1
Deduct 45 from 70 and we're left 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 can be fit into 250 5 times, resulting in a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 11314.15
Deduct 225 from 250 and we're left 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.

On to step 9:
The number 45 fits into 250 5 times, leaving a remainder of 25.
The next digit of our result is 5. 
Result so far: 11314.155
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The final result is 11314.155 with a remainder of 0.0025.