History of Writing Decimals and Number Lines
Date: 10/28/98 at 19:51:21 From: Kim Subject: Integers and decimals A student asked me why on a number line the negative numbers are on the left, and when you deal with decimals, the whole numbers are on the left. I am new to teaching math, and I understand his need to know but have a difficult time explaining it. Help!
Date: 10/29/98 at 12:31:04 From: Doctor Peterson Subject: Re: Integers and decimals Hi, Kim, This is one of those "why" questions that can be hard to answer. The basic answer is that there is no connection between the two. People just chose those directions. But it is interesting to think about why each is the way it is. The number line probably was first drawn before there were negative numbers. It would be natural to start at zero (or one) and count to the right, in countries that write from left to right. Then of course the negative numbers go on the left. The same sort of thing would have happened with decimal digits. Once people were used to writing integers with the least significant digit (the ones place) at the right, then when decimals were invented the decimal point would have to go to the right of that, and decimal places farther to the right. So the real question is simply, why are integers written left to right starting with the most significant digits? As far as I know, this is an old tradition, used not only in our arabic numerals but also in Roman, Greek, Egyptian, Babylonian, and whatever else there was. It makes some sense to start with the most important digits, just as you might start a list of people with the king, then his advisors, and so on down to the peasants. That's different from the number line, because there is no highest number to put down first on the line! You can't start at the high end, so you start at the low end, where there is a definite beginning (at least until negative numbers were invented) and you usually count up, not down. You and your student may be interested to know that computer designers have argued over the direction numbers should be "written" in the computer's memory. Many computers, such as the Motorola 68000 series microprocessors I work with (used in Macintosh), store the most significant digit first, the way we write them. This is called, in a humorous reference to a dispute in Gulliver's Travels over which end of an egg should be eaten first, the "big-endian" method. Others, such as the Intel series (used in PCs) store the least significant digit first, which makes a lot of sense for some purposes, such as when you don't know whether a small number is stored as 00000052 or as 52. On a "little-endian" computer, you just read the first two digits, regardless of whether it is stored as "25" or as "25000000". On a big- endian computer, you have to be told how it is stored. On the other hand, the big-endian method allows you to sort numbers the same way you alphabetize words, looking first at the leftmost digit and working your way to the right. So the choice of writing numbers in decreasing order of significance as we do is entirely arbitrary, but has some reasons behind it. Thanks for the question! Hope it stimulates some good conversations. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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