We look at the division of 46378 by 89 
We want to figure out the number of times 46378 can be divided by 89.

On to step 1:
If we divide 4 by 89, we get 0 and a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 89

On to step 2:
89 can be fit into 46 0 times, resulting in a remainder of 46.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 46 and we're left with 46.
Bring next digit (3) of the dividend behind the 46 and repeat the process: 463 / 89

Advancing to step 3:
89 can be fit into 463 5 times, resulting in a remainder of 18.
The next digit of our result is 5. 
Result so far: 5.0
If we take 445 away from 463, we end up with 18.
Grab the next digit (7) from the dividend, add it to 18, then carry on: 187 / 89

On to step 4:
89 goes into 187 2 times with a remainder of 9.
The next digit of our result is 2. 
Result so far: 52.0
The remainder is 9 after subtracting 178 from 187.
Append the next digit (8) from the dividend to 9 and continue with: 98 / 89

Step 5:
98 divided by 89 is 1 with a remainder of 9.
The next digit of our result is 1. 
Result so far: 521.0
Deduct 89 from 98 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 6:
89 goes into 90 1 times with a remainder of 1.
The next digit of our result is 1. 
Result so far: 521.1
If we take 89 away from 90, we end up 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.

On to step 7:
89 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 521.1
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.

Going ahead to step 8:
89 can be fit into 100 1 times, resulting in a remainder of 11.
Put 1 as the next digit of the answer. 
Result so far: 521.101
The remainder is 11 after subtracting 89 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 9:
The number 89 fits into 110 1 times, leaving a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 521.1011
Deduct 89 from 110 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

The quotient of the division is 521.1011, and the remainder is 0.00021.