We look at the division of 637118 by 45 
Let's see how many times 45 fits into 637118.

On to step 1:
45 can be fit into 6 0 times, resulting in a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 45

Step 2:
63 divided by 45 is 1 with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 45 from 63 to get 18.
Grab the next digit (7) from the dividend, add it to 18, then carry on: 187 / 45

Moving on to step 3:
187 divided by 45 is 4 with a remainder of 7.
Use 4 as the next digit of our solution. 
Result so far: 14.0
Subtract 180 from 187 to get 7.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 45

Advancing to step 4:
45 goes into 71 1 times with a remainder of 26.
Put 1 as the next digit of the answer. 
Result so far: 141.0
Deduct 45 from 71 and we're left with 26.
Take the next digit (1) from the dividend and append it to 26, then repeat: 261 / 45

Step 5:
45 goes into 261 5 times with a remainder of 36.
Put 5 as the next digit of the answer. 
Result so far: 1415.0
Subtract 225 from 261 to get 36.
Grab the next digit (8) from the dividend, add it to 36, then carry on: 368 / 45

Going ahead to step 6:
368 divided by 45 is 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 14158.0
If we take 360 away from 368, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 7:
The number 45 fits into 80 1 times, leaving a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 14158.1
Deduct 45 from 80 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 8:
The number 45 fits into 350 7 times, leaving a remainder of 35.
Write down 7 as next digit of the result. 
Result so far: 14158.17
Subtract 315 from 350 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 9:
350 divided by 45 is 7 with a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 14158.177
The remainder is 35 after subtracting 315 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

In conclusion, the division gives 14158.177 with a balance of 0.0035.