We're dividing 637781 by 10 
Let's see how many times 10 fits into 637781.

Let's proceed to step 1:
When dividing 6 by 10, we get 0 with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 10

On to step 2:
63 divided by 10 is 6 with a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 60 away from 63, we end up with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 10

Going ahead to step 3:
10 goes into 37 3 times with a remainder of 7.
The next digit of our result is 3. 
Result so far: 63.0
Deduct 30 from 37 and we're left with 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 10

On to step 4:
When dividing 77 by 10, we get 7 with a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 637.0
Subtracting 70 from 77 leaves us with 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 10

Step 5:
If we divide 78 by 10, we get 7 and a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 6377.0
The remainder is 8 after subtracting 70 from 78.
Append the next digit (1) from the dividend to 8 and continue with: 81 / 10

Advancing to step 6:
The number 10 fits into 81 8 times, leaving a remainder of 1.
The number 8 becomes the next digit in our result. 
Result so far: 63778.0
If we take 80 away from 81, we end up with 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 7:
10 divided by 10 is 1 with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 63778.1
Deduct 10 from 10 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 8:
10 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 63778.1
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 9:
When dividing 0 by 10, we get 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 63778.1
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 63778.1, with a leftover of 0.0.