7113 ÷ 71 
Let's see how many times 71 fits into 7113.

Advancing to step 1:
71 can be fit into 7 0 times, resulting in a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 71

On to step 2:
When dividing 71 by 71, we get 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 71 from 71 leaves us with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 71

Step 3:
1 divided by 71 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 71

Going ahead to step 4:
When dividing 13 by 71, we get 0 with a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 100.0
If we subtract 0 from 13, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 5:
130 divided by 71 is 1 with a remainder of 59.
Use 1 as the next digit of our solution. 
Result so far: 100.1
Deduct 71 from 130 and we're left with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Let's proceed to step 6:
When dividing 590 by 71, we get 8 with a remainder of 22.
Write down 8 as next digit of the result. 
Result so far: 100.18
The remainder is 22 after subtracting 568 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 7:
The number 71 fits into 220 3 times, leaving a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 100.183
Subtracting 213 from 220 leaves us 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.

Advancing to step 8:
When dividing 70 by 71, we get 0 with a remainder of 70.
The next digit of our result is 0. 
Result so far: 100.183
The remainder is 70 after subtracting 0 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 9:
The number 71 fits into 700 9 times, leaving a remainder of 61.
Use 9 as the next digit of our solution. 
Result so far: 100.18309
If we take 639 away from 700, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 10:
71 goes into 610 8 times with a remainder of 42.
Use 8 as the next digit of our solution. 
Result so far: 100.183098
The remainder is 42 after subtracting 568 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 11:
71 goes into 420 5 times with a remainder of 65.
The next digit of our result is 5. 
Result so far: 100.1830985
Subtracting 355 from 420 leaves us with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

On to step 12:
When dividing 650 by 71, we get 9 with a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 100.18309859
The remainder is 11 after subtracting 639 from 650.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

After the division, we end up with 100.18309859 and a remainder of 1.1e-08.