Order of Decimals

Date: 05/18/99 at 17:45:34
From: Catherine Eilidh Williams
Subject: How do you put decimals in order?

How in the world do you put decimals in order?  For example, 5.9, 
6.10, 2.52. I think it is very confusing.

Date: 05/19/99 at 08:26:51
From: Doctor Rick
Subject: Re: How do you put decimals in order?

Hi, Catherine.

In the example you gave, it's not so bad because you can ignore the 
decimal parts. Can you put 5, 6, and 2 in order? Once you've done 
this, put the decimals back on, and you're done.

That's always the first step in putting decimal numbers in order: put 
the whole-number parts in order. But it's not always the last step. 
If two or more numbers have the same whole-number part, you have to 
look at the tenths digit. Rearrange the numbers so the tenths digits 
are in order.

You may still not be done. If two or more numbers have the same whole-
number part AND the same tenth digit, you need to look at the 
hundredths digits and put THEM in order. If you have more digits, 
this process can keep going and going and going ...

Remember: if a number doesn't have a hundredths digit, such as 5.9 
for example, you can add a 0 in the hundredths place and this does not 
change the number. Use this 0 when you order the numbers.

Here is an example. The first column is my list of numbers. 

  5.9       2.52      2.52      2.52
  6.29    / 5.9     / 5.9       5.90
  2.52    \ 5.93    \ 5.93      5.93
  5.93    / 6.29      6.1       6.1
  6.25   |  6.25    / 6.29      6.25
  6.1     \ 6.1     \ 6.25      6.29
            -           -          -

The second column is what I have after I put the whole-number parts 
in order; I put brackets around the numbers that have the same whole-
number part. 

The third column is what I have after putting the tenths digits in 
order - I only rearranged numbers that were bracketed in the second 
column. Numbers that have the same whole-number part AND tenths digit 
are still bracketed.

The fourth column is what I have after putting the hundredths digits 
in order. Since there are no thousandths digits, I am done.

Putting numbers in order is a lot like alphabetizing words but the 
whole-number part works differently from when you alphabetize. When 
you alphabetize, you always compare the first letter, then the second 
letter, and so on. When you order numbers numerically, you compare 
the thousands digits, the hundreds digit, etc. But when you get to the 
decimal part, ordering numbers works exactly the same as 
alphabetizing: you start at the decimal point and work to the right.

I hope this helps! It can be confusing, I know. It helps to have a 
method and do it one step at a time, as I showed you.

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