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Understanding Rational and Irrational Numbers in Mathematics

Learn the difference between rational and irrational numbers, how to identify them, and their properties in this interactive tutorial. Explore examples and practice exercises to enhance your knowledge of number theory.

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Understanding Rational and Irrational Numbers in Mathematics

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  1. http://www.math.harvard.edu/~knill/mathmovies/swf/bartproblem.htmlhttp://www.math.harvard.edu/~knill/mathmovies/swf/bartproblem.html

  2. Natural counting numbers. Natural Numbers - 1, 2, 3, 4 … Whole Numbers - Natural counting numbers and zero. 0, 1, 2, 3 … Integers - Whole numbers and their opposites. … -3, -2, -1, 0, 1, 2, 3 … Rational Numbers - Integers, fractions, and decimals. Ex:

  3. Venn Diagram: Naturals, Wholes, Integers, Rationals Rationals Integers Wholes Naturals

  4. What are RATIONAL Numbers?

  5. A number that can be expressed as a fraction or ratio (rational). The numerator and the denominator of the fraction are both integers. When the fraction is divided out, it becomes a terminating or repeating decimal. (Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.) Rational Numbers

  6. Rational Number examples: 6 can be written as: 6/1 or 6.0 -2 can be written as: -2/1 or -2.0 ½ can be written as: 0.5 -5/4 can be written as: -1.25 2/3 can be written as: ---- .66

  7. What are IRRATIONAL Numbers?

  8. An irrational number can be written as a decimal, but not as a fraction. In decimal form, irrational numbers do not repeat in a pattern nor do they terminate. Irrational Numbers

  9. = 3.141592654….. = 1.414213562….. .6781011132… Examples of irrational numbers are:

  10. http://web.archive.org/web/20070818074103/http://regentsprep.org/Regents/Math/rational/Prat.htmhttp://web.archive.org/web/20070818074103/http://regentsprep.org/Regents/Math/rational/Prat.htm Practice

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