19978 ÷ 13 
We want to divide 19978 by 13.

Moving on to step 1:
The number 13 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 13

Step 2:
19 divided by 13 is 1 with a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 13 from 19, we get 6.
Include the next digit (9) from the dividend after 6, then repeat: 69 / 13

On to step 3:
69 divided by 13 is 5 with a remainder of 4.
Put 5 as the next digit of the answer. 
Result so far: 15.0
Subtracting 65 from 69 leaves us with 4.
Include the next digit (7) from the dividend after 4, then repeat: 47 / 13

Let's proceed to step 4:
The number 13 fits into 47 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 153.0
The remainder is 8 after subtracting 39 from 47.
Bring next digit (8) of the dividend behind the 8 and repeat the process: 88 / 13

Advancing to step 5:
When dividing 88 by 13, we get 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 1536.0
If we subtract 78 from 88, we get 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 6:
13 goes into 100 7 times with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 1536.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 1536.76
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 8:
13 can be fit into 120 9 times, resulting in a remainder of 3.
The next digit of our result is 9. 
Result so far: 1536.769
If we take 117 away from 120, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 9:
If we divide 30 by 13, we get 2 and a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 1536.7692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 10:
40 divided by 13 is 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 1536.76923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 11:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 1536.76923
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 12:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 1536.7692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 13:
90 divided by 13 is 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 1536.76923076
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 1536.76923076 with a remainder of 1.2e-08.