We divide 511414 by 71
Our goal is to divide 511414 by 71.

Moving on to step 1:
If we divide 5 by 71, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 71

Let's proceed to step 2:
71 goes into 51 0 times with 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 (1) from the dividend, add it to 51, then carry on: 511 / 71

On to step 3:
511 divided by 71 is 7 with a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtract 497 from 511 to get 14.
Fetch the next digit (4) from the dividend, attach it to 14 and continue: 144 / 71

Going ahead to step 4:
When dividing 144 by 71, we get 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 72.0
Deduct 142 from 144 and we're left with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 71

Going ahead to step 5:
71 goes into 21 0 times with a remainder of 21.
Record the quotient 0 as the next digit in the result. 
Result so far: 720.0
Deduct 0 from 21 and we're left with 21.
Append the next digit (4) from the dividend to 21 and continue with: 214 / 71

Let's proceed to step 6:
71 can be fit into 214 3 times, resulting in a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 7203.0
Deduct 213 from 214 and we're left 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:
If we divide 10 by 71, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 7203.0
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
The number 71 fits into 100 1 times, leaving a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 7203.01
If we take 71 away from 100, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 9:
If we divide 290 by 71, we get 4 and a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 7203.014
If we take 284 away from 290, we end up 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.

Let's proceed to step 10:
60 divided by 71 is 0 with a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 7203.014
Subtract 0 from 60 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 11:
71 can be fit into 600 8 times, resulting in a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 7203.01408
Deduct 568 from 600 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 12:
71 can be fit into 320 4 times, resulting in a remainder of 36.
Put 4 as the next digit of the answer. 
Result so far: 7203.014084
Subtract 284 from 320 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 13:
The number 71 fits into 360 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 7203.0140845
If we take 355 away from 360, we end up 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:
If we divide 50 by 71, we get 0 and a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 7203.0140845
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

In conclusion, the division gives 7203.0140845 with a balance of 5e-08.