We look at the division of 510138 by 69 
We're looking to find how many times 69 goes into 510138.

Going ahead to step 1:
5 divided by 69 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 69

Step 2:
69 can be fit into 51 0 times, resulting in a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 51 and we're left with 51.
Grab the next digit (0) from the dividend, add it to 51, then carry on: 510 / 69

Going ahead to step 3:
69 can be fit into 510 7 times, resulting in a remainder of 27.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtracting 483 from 510 leaves us with 27.
Grab the next digit (1) from the dividend, add it to 27, then carry on: 271 / 69

On to step 4:
69 can be fit into 271 3 times, resulting in a remainder of 64.
Record the quotient 3 as the next digit in the result. 
Result so far: 73.0
If we subtract 207 from 271, we get 64.
Grab the next digit (3) from the dividend, add it to 64, then carry on: 643 / 69

Advancing to step 5:
643 divided by 69 is 9 with a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 739.0
If we take 621 away from 643, we end up with 22.
Bring next digit (8) of the dividend behind the 22 and repeat the process: 228 / 69

Moving on to step 6:
69 goes into 228 3 times with a remainder of 21.
The next digit of our result is 3. 
Result so far: 7393.0
If we take 207 away from 228, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
210 divided by 69 is 3 with a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 7393.3
Deduct 207 from 210 and we're left 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.

Going ahead to step 8:
69 goes into 30 0 times with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 7393.3
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 9:
69 can be fit into 300 4 times, resulting in a remainder of 24.
The next digit of our result is 4. 
Result so far: 7393.304
Subtract 276 from 300 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 10:
240 divided by 69 is 3 with a remainder of 33.
Put 3 as the next digit of the answer. 
Result so far: 7393.3043
Subtracting 207 from 240 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Going ahead to step 11:
69 goes into 330 4 times with a remainder of 54.
The next digit of our result is 4. 
Result so far: 7393.30434
The remainder is 54 after subtracting 276 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Let's proceed to step 12:
69 can be fit into 540 7 times, resulting in a remainder of 57.
Record the quotient 7 as the next digit in the result. 
Result so far: 7393.304347
If we take 483 away from 540, we end up with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Advancing to step 13:
570 divided by 69 is 8 with a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 7393.3043478
If we take 552 away from 570, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 14:
69 can be fit into 180 2 times, resulting in a remainder of 42.
The number 2 becomes the next digit in our result. 
Result so far: 7393.30434782
If we take 138 away from 180, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

In conclusion, the division gives 7393.30434782 with a balance of 4.2e-08.