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### Defining Decimal Numbers

```Date: 07/01/2004 at 19:45:01
From: Michael
Subject: examples of decimals

Can you tell me examples of decimals?  Is 6.5 a decimal?  Is
3.141592.....a decimal?  I'm getting confused because I know that 6.5
has a whole number in it, so is it also a decimal?

```

```
Date: 07/01/2004 at 22:49:24
From: Doctor Peterson
Subject: Re: examples of decimals

Hi, Michael.

The word "decimal" is actually a very tricky one, and I'm not quite
sure that there is a correct answer to your question!  The word is
used so loosely that most uses of it are really wrong.  If you're
confused, it's because the world is confused.

Properly speaking, since the "deci-" in the word means "ten", ANY
number written in a base-ten system (that is, with each digit worth
ten times as much as the one next to it) can be called a "decimal
number".  When we write "123", the 3 is worth 3 ones, the 2 is worth
2 tens, and the 1 is worth a ten of tens, or a hundred.  That is
decimal.

But we also talk about "decimal fractions", which are non-whole
numbers written in that way, using a decimal point.  The trouble
comes when people shorten that to "decimals", dropping the part of
the phrase that really says what they want to say (that it is not a
whole number) and keeping the part that is true of any number we
write today.  A decimal fraction, also called a decimal, is a number
with a decimal point in it, like 1.23.

Then people talk about the "decimal part" of a number, which really
means the FRACTIONAL part, the non-whole part.  This is even worse,
making it sound like the 1 in 1.23 is not decimal while the .23 is.
The reality is that both parts are "decimal", but only the .23 is
fractional.  But the common usage can make us think that 1.23 is not
a decimal, but a mixed number, like 1 23/100, and that only numbers
less than 1, like .23, can be called decimals.  The point that
divides the two parts, of course, is called a "decimal point", when
what it marks is not really the start of the decimal part, but of
the fractional part.  I wish we called it something else, like
"fraction point".  But of course, a fraction is written like 23/100,
so that would be confusing too.

If you have heard about writing numbers in bases other than ten, such
as base 5, we can get really confused when we want to talk about
fractional numbers written in the place value system.  Are they "base
5 decimals", when "decimal" means "base ten"?  I don't think so!  But
we don't really have a good word for it.

I hope this hasn't just confused you more.  I just want to show why
you may get different answers to your question.  In my opinion, any
number with a decimal point in it would be commonly called a decimal,
not just a number less than 1.

When I answer a question about words, I like to check with a
dictionary, to see if the lexicographers, who define words for a
living, and constantly watch how words are really used, agree with
my impression.  Here is what Merriam-Webster (m-w.com) says:

Main Entry: decimal
Function: noun
:any real number expressed in base 10; especially: DECIMAL FRACTION

Main Entry: decimal fraction
Function: noun
:a fraction (as .25 = 25/100 or .025 = 25/1000) or mixed number
(as 3.025 = 3 25/1000) in which the denominator is a power of 10
usually expressed by use of the decimal point

I think they agree exactly with me:  a "decimal" is any number in base
10, but is usually used specifically for a number with a decimal

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Definitions
Elementary Place Value
High School Definitions
Middle School Definitions

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