The basic rule is, everytime you bring one digit down for division, you check for divisibility. So in this case, 12 is divisible and you get 3 on the side. When you bring the 3 down, 3 is NOT divisible by 4, so you put a zero on the quotient, before adding a 0 to the 3, making it 30 and then proceeding with the decimal point. In the first example, when you divide 11 by 4, you get 2, and you get a REMINDER from this which is 3, and then you bring the 3 down and hence check for divisibility of 33. And 33 > 4 so you add the 8 there.

Whenever you bring a digit down from the main number you're dividing you must check for divisibility. If the number you've brought down is less than the divisor itself, you add a zero. But in terms of checking for results, think about in terms of common sense. Does 3.75*4 being equal to something near 120 make sense? No. That's a way to cross check.

And just for reference, it's a miss. Not Mr.

Hope this helps. If not, refer the math book at GMAT Club for further references on the number properties and divisibility and so on.

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But why do i have to put 0 first in quotient side? I didn't do the same thing in Example1 before putting a point in quotient side.

You didn't add the zero because when you brought the 3 down, there was already a reminder there. So you made the number 33 and then added an 8 there. Here the initial reminder is a 0 and when you bring the 3 down, it stays as 03 and hence you add a 0 to the quotient because obviously 3 is not divisible by 4, being smaller than it.