TenMarks teaches you how to classify real numbers.
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Learn about Classification of Real Numbers In this lesson, let's learn how to classify real numbers. We tried different numbers and learned how to classify them. Let's start with 1/3. 1/3 is a real number. It's written as a/b, well we know b is not equal to zero. So I'm not dividing by zero. Whenever a number is represented as a/b, and if I divide them, 1/3, what do I get, 0.3333 and it goes on. So what does this mean? Since it's a repeating decimal, this becomes a repeating decimal number because the value of this is this but it's also a rational number because I can write this as 0.33 and I’ll have three be repeated all the way through. Remember that it's a rational number if it can be represented as a decimal with a value or a pattern repeating. Let's try Part B. Part B is 11. Well, that’s a pretty clear real number. This can be a whole number. It's a natural number. It's an integer. And it is of course a rational number because I can represent this as 11/1 and this is a terminating decimal because I could write this as 11.0. It terminates end, right? So that’s the classification for the number 11, all of these, for 1/3 is rational and repeating decimal. Let's try the third one which is square root of 14. Well 14 is not a perfect square. 3x3 is 9, 4x4 is 16. So 14 is not a perfect square. So the square root of 14 is going to be an irrational number because the square root of it is not a perfect square and chances of it being repeating are zero. So the classifications are, first, whether it's rational or irrational, and then we get into all of these. Let me actually just use a table to refresh your memory. So you either have rational numbers of irrational numbers. In rational numbers, some numbers will be integers which are whole numbers with positive and negative values. Zero followed by -1, -2, -3, +1, +2, +3, and so on. If you’ve got whole numbers which are zero, one, two, three etcetera, anything starting with zero and going on to infinity but no negative numbers. Then you have natural numbers which means they don’t include zero, the numbers that count. On the irrational side, you have things that are not repeating and non-terminating. So they will just go on forever but they will not be a pattern that repeats. So they cannot be expressed in a simple form like this. Actually they can be, but 22/7 for example p, it goes on forever. 27/4 does not, it ends at a certain point or repeats after a certain point. That’s the definition between rational and irrational. So when we think about classifying numbers, they need to be rational or irrational and if rational, they may be one or more of these.