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3 Digit Long Division

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					                              3 Digit Long Division

3 Digit Long Division
I am going to assume that you can handle smaller divisors and know the basic techniques of long
division, but need help on how to choose (guess) a digit to try in the quotient. Let us try your first
problem, and see how it goes.
     _______
   918)67932

The first set of digits bigger than 918 is 6793. We need to estimate the quotient 6793/918. To get a
rough estimate, you can just drop the last two digits from both numbers: 67/9 = 7. (Do you see why? It
is the same as approximating the fraction 6793/918 by 6700/900 and simplifying.) So let us try using 7
in the quotient: 7 * 918 = 6426, so we write
     ____7__
   918)67932
      6426
      ----
       367

That looks good: the remainder is positive (always a good sign) but less then 918. So we continue:

                                              Know More About :- Property of Real Number


   Math.Edurite.com                                                           Page : 1/3
     ____7__
   918)67932
      6426
      ----
       3672
Again, we can estimate 3672/918 by 36/9 = 4. Since the result is a whole number, I will not be
surprised if it is wrong; it will not take much increase in the dividend to push the quotient past 4. But let
us try it: 4 * 918 = 3672. Let us write it down:
     ____74_
   918)67932
      6426
      ----
       3672
       3672
       ----
         0
That was too easy; it did not let me demonstrate how to recover from a mistake. Since estimation plays
a big role here, you have to be prepared to make a wrong guess. Let us suppose I had somehow guessed
6 for the first digit:
     ____6__
   918)67932
      5508
      ----
      1285

When I see that my remainder (1285) is bigger than my divisor (918), I know I have to increase the
quotient; I will try 7 and it will be right. Suppose instead that I guessed 8:
    ____8__
  918)67932
     7344
     ----

                                          Read More About :- History of Real Numbers


    Math.Edurite.com                                                              Page : 2/3
     Thank You




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