We're dividing 7663 by 27 
We want to figure out the number of times 7663 can be divided by 27.

Advancing to step 1:
The number 27 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 27

On to step 2:
27 can be fit into 76 2 times, resulting in a remainder of 22.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 54 away from 76, we end up with 22.
Append the next digit (6) from the dividend to 22 and continue with: 226 / 27

Step 3:
226 divided by 27 is 8 with a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 28.0
If we subtract 216 from 226, we get 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 27

Moving on to step 4:
27 goes into 103 3 times with a remainder of 22.
The number 3 becomes the next digit in our result. 
Result so far: 283.0
The remainder is 22 after subtracting 81 from 103.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 5:
When dividing 220 by 27, we get 8 with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 283.8
If we subtract 216 from 220, 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.

Step 6:
The number 27 fits into 40 1 times, leaving a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 283.81
If we subtract 27 from 40, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
If we divide 130 by 27, we get 4 and a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 283.814
If we subtract 108 from 130, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 8:
220 divided by 27 is 8 with a remainder of 4.
The next digit of our result is 8. 
Result so far: 283.8148
If we take 216 away from 220, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 9:
If we divide 40 by 27, we get 1 and a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 283.81481
Subtracting 27 from 40 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 10:
27 goes into 130 4 times with a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 283.814814
Subtracting 108 from 130 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 11:
27 goes into 220 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 283.8148148
The remainder is 4 after subtracting 216 from 220.
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 12:
27 goes into 40 1 times with a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 283.81481481
Subtracting 27 from 40 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final result is 283.81481481 with a remainder of 1.3e-08.