We're dividing 141005 by 45 
We want to figure out the number of times 141005 can be divided by 45.

Going ahead to step 1:
The number 45 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 45

On to step 2:
The number 45 fits into 14 0 times, leaving a remainder of 14.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 14 after subtracting 0 from 14.
Append the next digit (1) from the dividend to 14 and continue with: 141 / 45

Advancing to step 3:
45 goes into 141 3 times with a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 135 from 141, we get 6.
Append the next digit (0) from the dividend to 6 and continue with: 60 / 45

Going ahead to step 4:
45 goes into 60 1 times with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 31.0
If we take 45 away from 60, we end up with 15.
Grab the next digit (0) from the dividend, add it to 15, then carry on: 150 / 45

Step 5:
If we divide 150 by 45, we get 3 and a remainder of 15.
Use 3 as the next digit of our solution. 
Result so far: 313.0
The remainder is 15 after subtracting 135 from 150.
Fetch the next digit (5) from the dividend, attach it to 15 and continue: 155 / 45

Step 6:
When dividing 155 by 45, we get 3 with a remainder of 20.
Put 3 as the next digit of the answer. 
Result so far: 3133.0
If we subtract 135 from 155, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 7:
If we divide 200 by 45, we get 4 and a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 3133.4
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
45 can be fit into 200 4 times, resulting in a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 3133.44
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Our division results in 3133.44 with a remaining 0.02.