Ordering Decimals

Date: 10/17/98 at 22:03:30
From: C. Dunham
Subject: Comparing and ordering decimals

My daugther is in 5th grade and is having a problem with comparing 
decimals. For example, is .467 less than, greater than, or equal to 
.465? What is the easiest way to teach her and for her to remember it?  

Date: 10/19/98 at 13:05:35
From: Doctor Peterson
Subject: Re: Comparing and ordering decimals

I think I would start with what she already knows about comparing whole 
numbers. To compare 467 and 465, she would line them up with the ones 
digits together:

   467
   465

and look for the first place where they are different, starting from 
the left. The 4's are the same, the 6's are the same, so the difference 
is between the 7 and the 5, making 467 bigger than 465. This is because 
the digits on the left are most "valuable." If you have more hundreds, 
it doesn't matter whether you have fewer tens.

To compare decimals you do exactly the same thing, as long as you 
remember to line up the ones digits (or the decimal points), not the 
rightmost digits, which might have different values. Here's an example 
of that:

   4.67
   4.654

I've lined up the decimal points; the 4's and the 6's match, so the 
first difference is in the hundredths place, where 7 > 5, so 
4.67 > 4.654.

So the keys are to make sure you are comparing hundreds with hundreds, 
and so on, and to start with the most valuable places. I think this 
method should give her both a comforting routine to follow, and an 
understanding of what it means, both of which are important.

Let me know whether that helps!

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