Adding Decimals

Date: 05/26/98 at 01:12:30
From: Jennifer
Subject: Adding decimals

I can't figure this out!

              894.56
            + 4563.5
            ---------

Date: 06/10/98 at 19:00:52
From: Doctor Mateo
Subject: Re: adding decimals

Hello Jennifer,

To add (or subtract decimals) the first thing you should do is line up 
the  decimal points.

                894.56
            +  4563.5
            -----------

It is important for you to line up the decimals vertically the way I 
did above so that you can keep track of the place-value position of 
the digits.

You could think about it like this.  

Suppose you have a WHOLE LOT of coins: pennies, nickles, dimes, and 
quarters.

There are lots of ways to count the money, but what is probably the 
fastest way to do it since you have a whole lot of change to count?

Probably separating the coins into stacks of pennies, stacks of 
nickles, stacks of dimes, and stacks of quarters, and then counting up 
the value of each stack. If you have enough of a certain coin you 
might even collect it in a coin holder.

So when you add (or subtract) decimals, we like to put our digits into 
"stacks" of similar values too.

If you remember, we like to put the digits into colums or "bundles" of 
powers of tens just the way we would put dimes with other dimes.
So in this example we place the numbers into their place-value holder
 
   
thousands // hundreds //  tens //  ones // . //  tenths // hundredths 

          //   8     //   9   //   4   // . //   5     //    6     
 
 +   4   //    5    //   6   //   3   // . //    5    //  
_____________________________________________________________________

After you line up the decimal points, you might want to put zeros in 
the empty spaces as space-holders, like this:
                 
               894.56
           +  4563.50
          --------------

One of the reasons we place zeros in the empty spaces after the 
decimal point is that we can have a record of the number of "coins" in 
that position. If you have no hundredths then you record a "0" to show 
that you had no hundredths to count.

Now you can do regular addition. Just make sure you bring the decimal 
point down in the same position it is in the problem.

Have fun adding.
          
-Doctor Mateo,  The Math Forum
 http://mathforum.org/dr.math/   

Date: 05/26/98 at 11:36:11
From: Doctor Barrus
Subject: Re: Adding decimals 

Hi, Jennifer!

Adding decimals isn't that different from adding whole numbers. There 
are just a few extra steps. I'm going to work a problem that's similar 
to yours, and then I hope you'll see how to do yours. 

Okay! Here's what we do. Say I have the problem:

992.536
+ 473.9
-------
   ?


1. The first thing to do is to line up the decimal points in a 
   straight vertical line. So I would rewrite my problem as

  992.536
+ 473.9
---------

with all the decimal points in a line.

2. Next, add as many zeroes as you need to "fill in the blanks" in the 
   decimal parts. For example, I would make my problem

  992.536
+ 473.900
---------

See how I filled in the empty spaces from step 1?  This works because 
473.9 = 473.900, just the way 1 = 1.0. Adding zeroes to the end of the 
decimal part of a number doesn't change the number.

3. Now add normally. The decimal point stays in that straight line, 
but the numbers just add following the normal rules, like carrying and 
stuff. So in my problem, I'd have

  992.536
+ 473.900
---------
 1466.436

I added this by just following the same steps I would to add

  992536
+ 473900
-------- ,

and I put the decimal point in the answer underneath all the other 
decimal points.


I hope this has helped. Go ahead and try your problem using the steps 
above. Good luck!

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