416681 ÷ 30 
Our goal is to divide 416681 by 30.

On to step 1:
When dividing 4 by 30, we get 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 30

Step 2:
If we divide 41 by 30, we get 1 and a remainder of 11.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 30 from 41 leaves us with 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 30

Advancing to step 3:
30 can be fit into 116 3 times, resulting in a remainder of 26.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
If we take 90 away from 116, we end up with 26.
Append the next digit (6) from the dividend to 26 and continue with: 266 / 30

Step 4:
When dividing 266 by 30, we get 8 with a remainder of 26.
Write down 8 as next digit of the result. 
Result so far: 138.0
The remainder is 26 after subtracting 240 from 266.
Fetch the next digit (8) from the dividend, attach it to 26 and continue: 268 / 30

On to step 5:
When dividing 268 by 30, we get 8 with a remainder of 28.
Record the quotient 8 as the next digit in the result. 
Result so far: 1388.0
If we subtract 240 from 268, we get 28.
Bring next digit (1) of the dividend behind the 28 and repeat the process: 281 / 30

Let's proceed to step 6:
The number 30 fits into 281 9 times, leaving a remainder of 11.
Record the quotient 9 as the next digit in the result. 
Result so far: 13889.0
Subtracting 270 from 281 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
If we divide 110 by 30, we get 3 and a remainder of 20.
Use 3 as the next digit of our solution. 
Result so far: 13889.3
If we subtract 90 from 110, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 8:
The number 30 fits into 200 6 times, leaving a remainder of 20.
The next digit of our result is 6. 
Result so far: 13889.36
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
When dividing 200 by 30, we get 6 with a remainder of 20.
The next digit of our result is 6. 
Result so far: 13889.366
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 13889.366 and a remainder of 0.002.