Real numbers that have a nonrepeating decimal

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Unformatted text preview: are calculated with any accuracy, but can’t be changed by a rational number. They can appear as results of geometrical measurements, for example: - a ratio of a square diagonal length to its side length is equal to - a ratio of a circumference length to its diameter length is an irrational number Examples of another irrational numbers: The Real Numbers The real numbers are those representable by an infinite decimal expansion, which may be repeating or nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes referred to as the continuum. Real numbers that have a nonrepeating decimal expansion are called irrational, i.e., they cannot be represented by any ratio of integers. The Greeks knew of the existence of irrational numbers through geometry; e.g., 2 is the length of the diagonal of a unit square. The proof that 2 is unable to be represented by such a ratio was the first proof of the existence of irrational numbers, and it caused tremendous upheaval in the mathematical thinking of that time. Imaginary and complex numbers Consider the pure quadratic equation: x2 = a , where a – a known value. Its solution may be presented as: Math I - 18 - Feel free to pass this on to your friends, but please don’t post it online. Discuss UPCAT and other college entrance exam questions and answers at Academic-Clinic’s Facebook Page. We encourage you to answer the questions we post there and actively participate in the discussions on our wall. For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam information, visit the Academic-Clinic website. Tell your friends and classmates to come find and join us. The more, the merrier. Good luck! AcademicAcademic Academic-Clinic.com The achiever’s guide to academic life and beyond… W ebsite: http://academic-clinic.com Facebook: http://www.facebook.com/academic.clinic Twitter: http://twitter.com/acadclinic College entrance exam and science high school entrance test tips. Conquer UPCAT, ACET, USTET, DLSUCET, PSHS-NCE, and other entrance tests. Here the three cases are pos...
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