Let's divide 343434 by 45
We want to divide 343434 by 45.

Advancing to step 1:
3 divided by 45 is 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 45

Advancing to step 2:
45 can be fit into 34 0 times, resulting in a remainder of 34.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 34, we get 34.
Include the next digit (3) from the dividend after 34, then repeat: 343 / 45

Advancing to step 3:
The number 45 fits into 343 7 times, leaving a remainder of 28.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 315 from 343, we get 28.
Bring next digit (4) of the dividend behind the 28 and repeat the process: 284 / 45

Let's proceed to step 4:
When dividing 284 by 45, we get 6 with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 76.0
If we take 270 away from 284, we end up with 14.
Append the next digit (3) from the dividend to 14 and continue with: 143 / 45

On to step 5:
When dividing 143 by 45, we get 3 with a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 763.0
Subtract 135 from 143 to get 8.
Grab the next digit (4) from the dividend, add it to 8, then carry on: 84 / 45

Step 6:
The number 45 fits into 84 1 times, leaving a remainder of 39.
The number 1 becomes the next digit in our result. 
Result so far: 7631.0
If we take 45 away from 84, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 7:
45 goes into 390 8 times with a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 7631.8
Subtracting 360 from 390 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
The number 45 fits into 300 6 times, leaving a remainder of 30.
The next digit of our result is 6. 
Result so far: 7631.86
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 9:
45 goes into 300 6 times with a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 7631.866
Subtracting 270 from 300 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

After the division, we end up with 7631.866 and a remainder of 0.003.