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 point. So the answer to your examples is "yes". If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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