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Learning Decimals


Date: 10/19/98 at 16:54:41
From: LEE 
Subject: Decimals

Hi,

My name is Lee. For the past few days, we have been learning decimals, 
and I don't understand them that well. What should I do?


Date: 10/19/98 at 20:45:54
From: Doctor Sam
Subject: Re: Decimals

Hi Lee!

Have you asked your teacher for extra help? I think finding another 
person to talk to is best. But in the meantime, maybe this will help a 
little.

When I think of decimals I sometimes think about money. Not all kinds 
of money, just certain kinds. For bills: $100 bills, $10 bills and 
$1 bills. For coins: pennies and dimes.

A decimal is a number that looks like this: 24.31  or 154.7

The "." is called the decimal point and it separates the decimal into 
two parts. The part on the left is an ordinary whole number, like 24 
or 154.

The part on the right is really a fraction, but never in quarters or 
thirds, always tenths or hundredths.  

Here is why I think about money. I can think about 154 this way:

   1 hundred dollar bill + 5 ten dollar bills + 4 one dollar bills

You can always break up any whole number this way. (Of course, bigger 
whole numbers have thousands and millions and there aren't bills that 
big, so money will only work with smaller numbers.)

I can think about the digits to the right of the decimal point this 
way:

  .56 means 5 dimes and 6 pennies

That's because a dime is one-tenth of a dollar and a penny is 
one-hundredth of a dollar.

So 176.28 means 1 (100) + 7 (10) = 6(1) + 2(tenths) + 8 (hundredths).  

Now decimal numbers can have lots more digits to the right (like 
4.51728) but we only have dimes and pennies, so you can't think about 
money to help you with those numbers.

But all decimal numbers are made up of whole number parts to the left 
of the decimal and fractional parts to the right. The whole numbers 
are always ten times bigger as you move to the left:
                                       
   ---------------   -----------     -----------    --------------- .
      thousands        hundreds         tens            ones 
        place           place           place           place

   1000 = 10 x 100   100 = 10x10     10 = 10 x 1    1 = 10 x (1/10)

and the fractions to the right of the decimal are all ten times 
smaller as you go to the right:

  . ------------      ------------           -------------   
       tenths          hundredths             thousandths    
       place             place                  place     
 
     1/10 =            1/100 =                1/1000 =    
     1 divided by 10   1/10 divided by 10     1/100 divided by 10


I hope that helps!

- Doctor Sam, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Fractions

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