Rational And Irrational Numbers

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Rational And Irrational Numbers Rational And Irrational Numbers

Rational Numbers A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1. Likewise, 3/4 is a rational number because it can be written as a fraction. Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction. Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1. Know More About Rational Numbers Properties

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Rational Numbers: - Every integer and fractions are rational numbers. It can always be denoted as p/q, where p and q are integers and q is not equal to 0. Thus for example the rationals include {0, 5/2, -18, -4/3, 27/5}. We unually write rational numbers in their lowest terms, for example 8/10 is usually written 4/5. We commonly write rationals in decimal form, so that 1/4 is the same as 0.25, 13/8 = 1.625 and 4/5 = 0.8. Some rationals, however, when written in decimal form don't stop a few places after the decimal. For example 1/3 = 0.333..., 10/11 = 0.909090... and 3/13 = 0.230769230769... When you write a rational number in decimal form you obtain either a decimal that stops after a finite number of terms, or a pattern that repeats as in the latter three examples. Irrational Numbers All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers: π = 3.141592… = 1.414213… Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers! Read More About Implicit Differentiation XY

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Irrational Numbers: - Infinite non-recurring decimal number can be expressed as an irrational number. If you construct a decimal that does not terminate and does not repeat it is not a rational number. For example 0.102003000400005... Numbers that are not rational are called irrational. The most famous of these is the ratio of the circumference of a circle to its diameter, called . is approximately 3.14159265358979323846; no matter how far we take the decimal expansion, it never repeats. Another irrational number is which is approximately 1.4142135623731.

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