770109 ÷ 77 
Let's see how many times 77 fits into 770109.

Going ahead to step 1:
When dividing 7 by 77, we get 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 77

On to step 2:
77 can be fit into 77 1 times, resulting in a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 77 from 77 to get 0.
Take the next digit (0) from the dividend and append it to 0, then repeat: 0 / 77

Moving on to step 3:
If we divide 0 by 77, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtract 0 from 0 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 77

Step 4:
If we divide 1 by 77, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 100.0
If we subtract 0 from 1, we get 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 77

Advancing to step 5:
When dividing 10 by 77, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 1000.0
Subtract 0 from 10 to get 10.
Bring next digit (9) of the dividend behind the 10 and repeat the process: 109 / 77

On to step 6:
The number 77 fits into 109 1 times, leaving a remainder of 32.
The number 1 becomes the next digit in our result. 
Result so far: 10001.0
If we subtract 77 from 109, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 7:
320 divided by 77 is 4 with a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 10001.4
If we take 308 away from 320, 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.

Step 8:
If we divide 120 by 77, we get 1 and a remainder of 43.
Put 1 as the next digit of the answer. 
Result so far: 10001.41
The remainder is 43 after subtracting 77 from 120.
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 9:
77 can be fit into 430 5 times, resulting in a remainder of 45.
Record the quotient 5 as the next digit in the result. 
Result so far: 10001.415
The remainder is 45 after subtracting 385 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Let's proceed to step 10:
450 divided by 77 is 5 with a remainder of 65.
Write down 5 as next digit of the result. 
Result so far: 10001.4155
Subtracting 385 from 450 leaves us with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

In conclusion, the division gives 10001.4155 with a balance of 0.00065.