We look at the division of 542456 by 588 
We want to figure out the number of times 542456 can be divided by 588.

Step 1:
588 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 588

Moving on to step 2:
If we divide 54 by 588, we get 0 and a remainder of 54.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 54, we get 54.
Fetch the next digit (2) from the dividend, attach it to 54 and continue: 542 / 588

Step 3:
If we divide 542 by 588, we get 0 and a remainder of 542.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 542, we end up with 542.
Grab the next digit (4) from the dividend, add it to 542, then carry on: 5424 / 588

Let's proceed to step 4:
The number 588 fits into 5424 9 times, leaving a remainder of 132.
The next digit of our result is 9. 
Result so far: 9.0
Subtracting 5292 from 5424 leaves us with 132.
Take the next digit (5) from the dividend and append it to 132, then repeat: 1325 / 588

On to step 5:
The number 588 fits into 1325 2 times, leaving a remainder of 149.
Use 2 as the next digit of our solution. 
Result so far: 92.0
Subtracting 1176 from 1325 leaves us with 149.
Take the next digit (6) from the dividend and append it to 149, then repeat: 1496 / 588

Let's proceed to step 6:
1496 divided by 588 is 2 with a remainder of 320.
Use 2 as the next digit of our solution. 
Result so far: 922.0
Subtract 1176 from 1496 to get 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3200, and continue the process.

Going ahead to step 7:
When dividing 3200 by 588, we get 5 with a remainder of 260.
Record the quotient 5 as the next digit in the result. 
Result so far: 922.5
Subtracting 2940 from 3200 leaves us with 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2600, and continue the process.

Let's proceed to step 8:
The number 588 fits into 2600 4 times, leaving a remainder of 248.
Use 4 as the next digit of our solution. 
Result so far: 922.54
Subtract 2352 from 2600 to get 248.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2480, and continue the process.

On to step 9:
588 goes into 2480 4 times with a remainder of 128.
The number 4 becomes the next digit in our result. 
Result so far: 922.544
If we take 2352 away from 2480, we end up with 128.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1280, and continue the process.

In conclusion, the division gives 922.544 with a balance of 0.0128.