We're dividing 502674 by 7 
We want to divide 502674 by 7.

Step 1:
5 divided by 7 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 7

Going ahead to step 2:
If we divide 50 by 7, we get 7 and a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 49 from 50 leaves us with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 7

On to step 3:
The number 7 fits into 12 1 times, leaving a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 71.0
Deduct 7 from 12 and we're left with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 7

Moving on to step 4:
7 can be fit into 56 8 times, resulting in a remainder of 0.
The number 8 becomes the next digit in our result. 
Result so far: 718.0
If we subtract 56 from 56, we get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 7

Advancing to step 5:
7 can be fit into 7 1 times, resulting in a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 7181.0
Subtracting 7 from 7 leaves us with 0.
Take the next digit (4) from the dividend and append it to 0, then repeat: 4 / 7

On to step 6:
When dividing 4 by 7, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 71810.0
Subtract 0 from 4 to 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 7:
The number 7 fits into 40 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 71810.5
If we subtract 35 from 40, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 8:
The number 7 fits into 50 7 times, leaving a remainder of 1.
The next digit of our result is 7. 
Result so far: 71810.57
Subtracting 49 from 50 leaves us 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.

Let's proceed to step 9:
10 divided by 7 is 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 71810.571
Subtracting 7 from 10 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 10:
7 can be fit into 30 4 times, resulting in a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 71810.5714
Subtract 28 from 30 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 11:
If we divide 20 by 7, we get 2 and a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 71810.57142
Deduct 14 from 20 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 12:
When dividing 60 by 7, we get 8 with a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 71810.571428
If we take 56 away from 60, 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.

On to step 13:
40 divided by 7 is 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 71810.5714285
Deduct 35 from 40 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 14:
50 divided by 7 is 7 with a remainder of 1.
The next digit of our result is 7. 
Result so far: 71810.57142857
Subtracting 49 from 50 leaves us 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.

In conclusion, the division gives 71810.57142857 with a balance of 1e-09.