We're dividing 6289 by 9 
We want to figure out the number of times 6289 can be divided by 9.

Step 1:
When dividing 6 by 9, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Fetch the next digit (2) from the dividend, attach it to 6 and continue: 62 / 9

Going ahead to step 2:
9 goes into 62 6 times with a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
The remainder is 8 after subtracting 54 from 62.
Grab the next digit (8) from the dividend, add it to 8, then carry on: 88 / 9

Advancing to step 3:
The number 9 fits into 88 9 times, leaving a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 69.0
Deduct 81 from 88 and we're left with 7.
Fetch the next digit (9) from the dividend, attach it to 7 and continue: 79 / 9

Let's proceed to step 4:
If we divide 79 by 9, we get 8 and a remainder of 7.
The next digit of our result is 8. 
Result so far: 698.0
Deduct 72 from 79 and we're left 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.

On to step 5:
The number 9 fits into 70 7 times, leaving a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 698.7
If we subtract 63 from 70, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 6:
The number 9 fits into 70 7 times, leaving a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 698.77
The remainder is 7 after subtracting 63 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 698.77, and the remainder is 0.007.