Multiplication

Date: 02/11/99 at 17:37:23
From: Karen Tornquist
Subject: Multiplication

How many decimal places should there be in this problem?

   3.26
 x 0.25

Date: 02/12/99 at 10:51:07
From: Doctor Micah
Subject: Re: Multiplication

Thanks for writing to Dr. Math. Decimals can be tricky, but once you 
learn the rules they aren't so bad. I assume you already know how to 
multiply two large numbers, such as 327 * 45. If you don't, please 
write back and we'll explain that also. If you do know how, then 
multiplying decimals is easy. Just forget about them and do the 
multiplication the way you normally would for two big numbers. Then add 
the number of decimal places in each of the numbers you started with.  
This is how many places from the right you should place the decimal in 
your result.  

Here's an example:

                      4.25
                    x 1.53        Now, just leave out the 
                    ------        decimals and multiply normally.

                       425
                     x 153
                     -----
                      1275
                     21250
                   + 42500
                   -------
                     65025        Now since 4.25 had two decimal 
                                  places and 1.53 had two decimal 
                                  places, the answer should have 
                                  2 + 2 = 4 decimal places. So:

                      4.25
                    x 1.53
                   -------
                    6.5025

The only time it's tricky is when your answer ends with zeroes. You 
have to be sure not to drop the zeroes before you put in the decimal 
point:

                     0.45
                    x   2         Do the same thing; just forget about
                    -----         the decimal and multiply.

                       45
                     x  2
                     ----
                       90         Now, the answer should have 
                                  0 + 2 = 2 decimal places. So:

                     0.45
                    x   2
                    -----
                     0.90         AFTER you add the decimal point,
                                  you can drop the ending zeroes. So:
 
                     0.45
                    x   2
                    -----
                      0.9

I hope you can do your own problem now.  If you still have trouble, 
please feel free to write back to Dr. Math.              

Good luck,

- Doctor Micah, The Math Forum
  http://mathforum.org/dr.math/