159874 ÷ 81 
Our goal is to divide 159874 by 81.

Advancing to step 1:
1 divided by 81 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 81

Going ahead to step 2:
15 divided by 81 is 0 with a remainder of 15.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 15 after subtracting 0 from 15.
Grab the next digit (9) from the dividend, add it to 15, then carry on: 159 / 81

Moving on to step 3:
When dividing 159 by 81, we get 1 with a remainder of 78.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 78 after subtracting 81 from 159.
Bring next digit (8) of the dividend behind the 78 and repeat the process: 788 / 81

Advancing to step 4:
The number 81 fits into 788 9 times, leaving a remainder of 59.
Write down 9 as next digit of the result. 
Result so far: 19.0
If we subtract 729 from 788, we get 59.
Bring next digit (7) of the dividend behind the 59 and repeat the process: 597 / 81

Step 5:
When dividing 597 by 81, we get 7 with a remainder of 30.
Record the quotient 7 as the next digit in the result. 
Result so far: 197.0
Subtract 567 from 597 to get 30.
Grab the next digit (4) from the dividend, add it to 30, then carry on: 304 / 81

Going ahead to step 6:
304 divided by 81 is 3 with a remainder of 61.
The number 3 becomes the next digit in our result. 
Result so far: 1973.0
Deduct 243 from 304 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 7:
If we divide 610 by 81, we get 7 and a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 1973.7
Deduct 567 from 610 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Advancing to step 8:
81 can be fit into 430 5 times, resulting in a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 1973.75
The remainder is 25 after subtracting 405 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 9:
81 can be fit into 250 3 times, resulting in a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 1973.753
Subtracting 243 from 250 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 10:
The number 81 fits into 70 0 times, leaving a remainder of 70.
Record the quotient 0 as the next digit in the result. 
Result so far: 1973.753
Subtracting 0 from 70 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 11:
When dividing 700 by 81, we get 8 with a remainder of 52.
The number 8 becomes the next digit in our result. 
Result so far: 1973.75308
If we take 648 away from 700, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 12:
81 can be fit into 520 6 times, resulting in a remainder of 34.
The number 6 becomes the next digit in our result. 
Result so far: 1973.753086
Subtract 486 from 520 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
When dividing 340 by 81, we get 4 with a remainder of 16.
The number 4 becomes the next digit in our result. 
Result so far: 1973.7530864
The remainder is 16 after subtracting 324 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 14:
160 divided by 81 is 1 with a remainder of 79.
The number 1 becomes the next digit in our result. 
Result so far: 1973.75308641
If we take 81 away from 160, we end up with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

In conclusion, the division gives 1973.75308641 with a balance of 7.9e-08.