We look at the division of 376641 by 88 
Let's see how many times 88 fits into 376641.

Moving on to step 1:
88 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 88

Going ahead to step 2:
37 divided by 88 is 0 with a remainder of 37.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Append the next digit (6) from the dividend to 37 and continue with: 376 / 88

On to step 3:
The number 88 fits into 376 4 times, leaving a remainder of 24.
Use 4 as the next digit of our solution. 
Result so far: 4.0
If we take 352 away from 376, we end up with 24.
Bring next digit (6) of the dividend behind the 24 and repeat the process: 246 / 88

Advancing to step 4:
88 goes into 246 2 times with a remainder of 70.
Record the quotient 2 as the next digit in the result. 
Result so far: 42.0
Deduct 176 from 246 and we're left with 70.
Bring next digit (4) of the dividend behind the 70 and repeat the process: 704 / 88

Advancing to step 5:
88 can be fit into 704 8 times, resulting in a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 428.0
Subtract 704 from 704 to get 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 88

Advancing to step 6:
When dividing 1 by 88, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 4280.0
Subtracting 0 from 1 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
88 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 4280.0
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
88 goes into 100 1 times with a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 4280.01
If we subtract 88 from 100, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 9:
88 can be fit into 120 1 times, resulting in a remainder of 32.
Use 1 as the next digit of our solution. 
Result so far: 4280.011
Subtract 88 from 120 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final outcome is 4280.011, with a leftover of 0.0032.