Decimal Division

Date: 09/02/97 at 16:08:53
From: Leah
Subject: Decimal division

How do I divide with numbers that have decimals in them?

Date: 09/08/97 at 13:52:23
From: Doctor Rob
Subject: Re: decimal division

First, learn how to divide a decimal by a whole number. You do this
by ignoring the decimal at first, and then, at the end, inserting the
decimal point in the answer directly above the decimal point in the
dividend.

Example:

              3 7.2 3 4 8
      -------------------
4 2 8 ) 1 5 9 3 6.4 9 4 4
        1 2 8 4
        ---------
          3 0 9 6
          2 9 9 6
          ---------
            1 0 0 4
              8 5 6
            ---------
              1 4 8 9
              1 2 8 4
              ---------
                2 0 5 4
                1 7 1 2
                ---------
                  3 4 2 4
                  3 4 2 4
                  -------
                        0

Once you have figured how to do that, you can next do a decimal
divided into a decimal.  You just need to remember two things:

  (1) x divided by y is the same as 10*x divided by 10*y. This is 
      because (10*x)/(10*y) = x/y.

  (2) To multiply by 10, move the decimal point one place to the 
      right. This is because we use base 10 in our numeral system.

To divide 3.77 into 211.87777, you get the same answer as dividing
37.7 into 2118.7777 (using (1) and (2) once), which is the same as
dividing 377 into 21187.777 (using (1) and (2) again).  Now doing the
division,

              5 6.2 0 1
      -----------------
3 7 7 ) 2 1 1 8 7.7 7 7
        1 8 8 5
        ---------
          2 3 3 7
          2 2 6 2
          ---------
              7 5 7
              7 5 4
              -------
                  3 7
                    0
                  -----
                  3 7 7
                  3 7 7
                  -----
                      0

So the answer is 56.201.

The way most people do this is to: (1) write the division problem in 
the usual way,

      -----------------
3.7 7 ) 2 1 1.8 7 7 7 7
     ^           ^

then (2) move the decimal in the divisor to the right to make it 
a whole number, then (3) move the decimal in the dividend the 
exact same number of places to the right, then (4) do the division, 
then (5) place the decimal point in the answer. Oftentimes the 
moved decimal point is designated with a small "caret" sign (which 
is an upside-down v, or an up-pointing arrow head, like this: "^") 
between two digits, and with the point down low where the decimal 
point would be.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/