plz tell me a clear difference b\w rational irrrational and polynomial plzzz with examples

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- Jan 4th 2008, 06:45 AM #1

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- Jan 4th 2008, 06:59 AM #2

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Rational numbers can be represented by a/b, where a and b are integers.

$\displaystyle \frac{2}{3}, \frac{99}{1170} $ are examples. If you write it in decimal form, it is either terminating, e.g. 1/2=0.5 or non-terminating but repeating, e.g. 1/3=0.333333....

IRRational numbers, when represented in decimal form is non-terminating and non-repeating. It cannot be represented as a/b for any integers a,b. Examples are $\displaystyle \sqrt{2}, 5\sqrt{3}, \pi$

Polynomials are of the form $\displaystyle a_{0}+a_{1}x^{1}+...+a_{n}x^{n}$ where x are variables or indeterminates and $\displaystyle a_{i}s $ are real numbers and x are natural numbers. For example, $\displaystyle 3x^{3} + 2x +7$. Here, $\displaystyle a_{0}=7, a_{1}=2, a_{2}=0, a_{3}=3$.

NOte that the exponents of x should be natural numbers for it to be a polynomial

- Jan 4th 2008, 07:04 AM #3
A polynomial is an algebraic equation such as: $\displaystyle ax^2+bx+c$

Rational numbers can be expressed as a fraction of integers: $\displaystyle \frac{a}{b}$

Irrational numbers cannot be expressed as a fraction of integers such as: $\displaystyle \pi$ or $\displaystyle e$

- Jan 4th 2008, 11:02 AM #4

- Jan 4th 2008, 04:36 PM #5

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