212 b Number theory helps scientists and researchers model problems. 5 Sections 5. 1 Number Theory 5. 2 The Integers 5. 3 The Rational Numbers 5. 4 The Irrational Numbers 5. 5 Real Numbers and Their Properties 5. 6 Rules of Exponents and Scientific Notation 5. 7 Arithmetic and Geometric Sequences 5. 8 The Fibonacci Sequence and the Golden Ratio Every time we use a computer, make a telephone call, or watch television we use a device that relies on numbers to operate. In addition to playing many roles in our everyday lives, numbers are also used to describe the natural world, communicate information, and describe problems facing scientists and researchers. In this chapter, we will see how number theory, the study of numbers and their properties, makes all these roles possible. Number theory has many applications that help scientists and researchers solve problems in many areas including communications, biology, medicine, computers, and other modern technical devices. Number theory is also used by architects to design concert hall ceilings for optimal acoustics. Why This Is Important Number Theory and the Real Number System Stuart Jenner/Shutterstock
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