Rational And Irrational Numbers Rational And Irrational 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. Irrational Numbers
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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! 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. RATIONAL AND IRRATIONAL NUMBERS Real and imaginary numbers make up the number system of algebra. Imaginary numbers are discussed in chapter 15 of this course. Read More About Rational Expressions Calculator
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Real numbers are either rational or irrational. The word RATIONAL comes from the word "ratio." A number is rational if it can be expressed as the quotient, or ratio, of two whole numbers. Rational numbers include fractions like 2/7, whole numbers, and radicals if the radical sign is removable. Any whole number is rational. Its denominator is 1. For instance, 8 equals , which is the quotient of two integers. A number like is rational, since it can be expressed as the quotient of two integers in the form . The following are also examples of rational numbers:
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