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Understanding Real Numbers: Rational, Irrational, and Their Interactions

Dive into the fascinating world of real numbers, where we explore the distinct categories of rational and irrational numbers. Learn about natural numbers (1, 2, 3, ...), whole numbers (including 0), integers (like -2 and -783), and how they relate to fractions and decimals. Discover the differences between repeating and terminating decimals versus non-repeating and non-terminating decimals. This comprehensive guide will enhance your understanding of number systems and their applications in mathematics.

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Understanding Real Numbers: Rational, Irrational, and Their Interactions

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  1. Real Numbers Rational / Irrational

  2. Real Numbers

  3. Real Numbers Rational Irrational

  4. Real Numbers Rational Irrational Natural #s 1,2,3,4,… (counting #s)

  5. Real Numbers Rational Irrational Whole #s 0 Natural #s 1,2,3,4,… (counting #s)

  6. Real Numbers Rational Irrational Integers -783 -2 Whole #s 0 Natural #s 1,2,3,4,… (counting #s)

  7. Real Numbers Rational Irrational Integers -783 -2 Whole #s 0 Natural #s 1,2,3,4,… (counting #s) Fractions

  8. Real Numbers Decimals – repeating & termination Rational Irrational Integers -783 -2 Whole #s 0 Natural #s 1,2,3,4,… (counting #s) Fractions

  9. Real Numbers Decimals – repeating & termination Rational Irrational Decimals – non-repeating & non-terminating Integers -783 -2 Whole #s 0 Natural #s 1,2,3,4,… (counting #s) Fractions

  10. Real Numbers Decimals – repeating & termination Rational Irrational Decimals – non-repeating & non-terminating Integers -783 -2 Whole #s 0 Natural #s 1,2,3,4,… (counting #s) Fractions Non-Real Numbers Imaginary #s

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