We look at the division of 378421 by 87 
We want to divide 378421 by 87.

Step 1:
The number 87 fits into 3 0 times, leaving 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.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 87

On to step 2:
If we divide 37 by 87, we get 0 and a remainder of 37.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Bring next digit (8) of the dividend behind the 37 and repeat the process: 378 / 87

Step 3:
The number 87 fits into 378 4 times, leaving a remainder of 30.
Put 4 as the next digit of the answer. 
Result so far: 4.0
The remainder is 30 after subtracting 348 from 378.
Grab the next digit (4) from the dividend, add it to 30, then carry on: 304 / 87

Going ahead to step 4:
If we divide 304 by 87, we get 3 and a remainder of 43.
The next digit of our result is 3. 
Result so far: 43.0
If we subtract 261 from 304, we get 43.
Fetch the next digit (2) from the dividend, attach it to 43 and continue: 432 / 87

Advancing to step 5:
87 can be fit into 432 4 times, resulting in a remainder of 84.
The number 4 becomes the next digit in our result. 
Result so far: 434.0
Deduct 348 from 432 and we're left with 84.
Include the next digit (1) from the dividend after 84, then repeat: 841 / 87

Advancing to step 6:
87 goes into 841 9 times with a remainder of 58.
Record the quotient 9 as the next digit in the result. 
Result so far: 4349.0
The remainder is 58 after subtracting 783 from 841.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Advancing to step 7:
When dividing 580 by 87, we get 6 with a remainder of 58.
Use 6 as the next digit of our solution. 
Result so far: 4349.6
The remainder is 58 after subtracting 522 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Advancing to step 8:
87 goes into 580 6 times with a remainder of 58.
The next digit of our result is 6. 
Result so far: 4349.66
Subtract 522 from 580 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The final outcome is 4349.66, with a leftover of 0.058.