We're dividing 821410 by 45 
Our goal is to divide 821410 by 45.

Moving on to step 1:
When dividing 8 by 45, we get 0 with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Grab the next digit (2) from the dividend, add it to 8, then carry on: 82 / 45

Moving on to step 2:
82 divided by 45 is 1 with a remainder of 37.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 45 from 82, we get 37.
Fetch the next digit (1) from the dividend, attach it to 37 and continue: 371 / 45

Advancing to step 3:
The number 45 fits into 371 8 times, leaving a remainder of 11.
The number 8 becomes the next digit in our result. 
Result so far: 18.0
Subtract 360 from 371 to get 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 45

On to step 4:
When dividing 114 by 45, we get 2 with a remainder of 24.
Record the quotient 2 as the next digit in the result. 
Result so far: 182.0
Subtracting 90 from 114 leaves us with 24.
Bring next digit (1) of the dividend behind the 24 and repeat the process: 241 / 45

Moving on to step 5:
241 divided by 45 is 5 with a remainder of 16.
Use 5 as the next digit of our solution. 
Result so far: 1825.0
The remainder is 16 after subtracting 225 from 241.
Bring next digit (0) of the dividend behind the 16 and repeat the process: 160 / 45

Advancing to step 6:
45 goes into 160 3 times with a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 18253.0
The remainder is 25 after subtracting 135 from 160.
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:
If we divide 250 by 45, we get 5 and a remainder of 25.
The next digit of our result is 5. 
Result so far: 18253.5
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.

Going ahead to step 8:
The number 45 fits into 250 5 times, leaving a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 18253.55
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.

Our division results in 18253.55 with a remaining 0.025.