Finding Numbers Between Decimals

Date: 08/13/98 at 17:49:37
From: VALDEMAR
Subject: Problem-Solving with Decimals

How do I find 3 decimals that are greater than 3.71 but less than 
3.72? Please explain.

Thank you,
Val

Date: 08/14/98 at 12:52:38
From: Doctor Peterson
Subject: Re: Problem-Solving with Decimals

Hi, Val. 

It sounds like this problem is intended to introduce you to the magic 
of decimals. The closer you look at the number line, the more numbers 
you can see. Here's how it works.

Start with a normal number line, showing only integers (whole numbers):

   0     1     2     3     4     5     6     7     8     9    10
   +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+


Now look more closely at the space between 3 and 4, by showing one 
decimal place:

  3.0   3.1   3.2   3.3   3.4   3.5   3.6   3.7   3.8   3.9   4.0
   +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+


Now look even more closely at the space between 3.7 and 3.8, by showing 
two decimal places:

  3.70  3.71  3.72  3.73  3.74  3.75  3.76  3.77  3.78  3.79  3.80     
   +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+


Do you see how each decimal place lets you see more numbers in between 
the numbers you've already seen?

Now it's your turn. Look between 3.71 and 3.72 and see what you can 
find. There are lots of numbers in there. The only hard part is to 
choose!

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/