# why do we call a decimal a decimal An ordinal number answers the question Which one? We will now see that the ordinal numbers express division into equal parts. An ordinal number names
which part -- the third part, the fourth, the fifth, and so on. If we divide 15, for example, into three equal parts -- into three 5's -- then we say that 5 is the of 15. We say that because 15 is the of 5: 5, 10, 15. We use that same to name the part. If we divide a quantity into four equal parts, then we call each part a ; if into five equal parts, a ; if into one hundred equal parts, a ; but if into two equal parts, we say. And so with the exception of half, an ordinal number indicates into how many parts a quantity has been divided. A third, a fourth, a fifth, and so on, are the names of parts. Those names belong to language itself, not just to mathematics. Those ordinals are prior to the names of numbers we call fractions, which, we are about to see, are numbers we need for measuring, and are the parts of number 1. We will go into this more in. Since our numbering system is based on the, it is called a system. Decem in Latin means ten. In the previous Lessons we learned about whole numbers, which are the repeated additions of 1: 1, 2, 3, 4, and so on. Here we will learn about numbers that are less than 1. They are the numbers we create when we divide 1 into equal parts -- where 1 is now a unit. And since this is a decimal system, those parts of 1 will have the names of the powers of 10: tenths, hundredths, thousandths, and so on. First, we will divide One into ten equal parts, and so each part is called a Tenth. If we divide each Tenth into ten equal parts, then One will be in one hundred equal parts -- count them And so we have divided One into Hundredths. If we divide each Hundredth into ten equal parts, then each tiny piece will be a Thousandth part of One. And so on. Those Tenths, Hundredths, Thousandths are called the. Let's examine these two special periods, Aren't all fractions recurring? is exactly 0 50000000. This will also apply to every terminating decimal fraction. So can't we say that all? Yes, we can! But mathematicians always ignore this special period of just zeroes and just say that "the decimal terminates" because they choose to write the number as a finite collection of decimal digits rather than an infinite one when there is a choice. 0. 49999999. 0. 4 0. 5 's never ends, we have another way in which all terminating decimals may be written as recurring ones - always replace the last non-zero digit, of a terminating decimal fraction by 's. 1/8 = 0 125 = 0 1249999999. Again, this reasoning is correct. Mathematically though, we do not use a period of in our decimal fractions but again choose to write it as a finite sequence of digits wherever possible (i. e. so that it terminates). It's really a matter of taste as both arguments are correct. Such decisions are made, choosing one as the preferred method, so that we can all conveniently talk the same mathematical language. These choices are called conventions. The same is true when deciding on which side of the road to drive. It is a convention in the UK that we drive on the left, but the convention in France is to drive on the right. So long as you go with the convention when driving in Britain and go with the other convention when in France, then there is no problem. But make sure you know which convention is being used in any other country!

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