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Understanding Real Numbers: Math 8H Test and Extra Credit Opportunity

Learn about real numbers, natural numbers, whole numbers, integers, and rational vs. irrational numbers. Test explanation and extra credit opportunity included.

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Understanding Real Numbers: Math 8H Test and Extra Credit Opportunity

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  1. 1-A8 Warm Up • 1. • -15 – 6 – [-4 – (-6)] • 3. a2 + b – c when a = -6, b = 5, c = -3 • Take your test home tonight and get a parent signature. • Return the test by tomorrow to get 2 extra credit points!

  2. Math 8H 1-8 Number Systems Algebra 1 Glencoe McGraw-Hill JoAnn Evans

  3. What are real numbers? Real Numbers

  4. Natural Numbers Natural Numbers: “Counting Numbers” 1, 2, 3, 4, 5, …

  5. Whole Numbers Natural Numbers Whole Numbers: Natural Numbers and 0 0, 1, 2, 3, 4, …

  6. Integers: Positive and Negative Whole Numbers …-3, -2, -1, 0, 1, 2,…

  7. Rational Numbers can be written as: When written as decimals they either repeat or terminate. Rational Numbers

  8. Rational Numbers Irrational Numbers Ex: These must be represented by a symbol (ex: ), or as a rounded number, or in radical form because the decimal doesn’t repeat or terminate (stop).

  9. Rational and Irrational Numbers are… Rational Numbers Irrational Numbers Real Numbers

  10. So what isn’t a real number? • When you divide by zero and get no • solution • = i (imaginary numbers)

  11. Do you remember the closure property? A set of numbers is CLOSED under an operation if the result of the operation (the answer) is in the same number set as the two numbers used in the operation.

  12. Determine whether each set of numbers is closed under the indicated operation: Is the set of whole numbers closed under the operation of multiplication? (When you multiply a whole numbertimes another whole number, is the answer always a whole number?) Remember, the whole numbers are 0, 1, 2, 3, … Closed

  13. Is the set of integers closed under the operation of division? (When you divide an integerbyanother integer, is the answer always an integer?) Remember, integers are all positive and negative whole numbers, including 0. Not closed. A counterexample:

  14. Is the set of irrational numbers closed under the operation of multiplication? (When you multiply an irrational numbertimes another irrational number, is the answer always an irrational number?) Remember, irrational numbers are numbers like pi or non-repeating and non-terminating decimals. Not closed. A counterexample to try on your calculator:

  15. Name the set of numbers to which each real number belongs. Example 1 Example 3 Example 2 Example 4 rational natural rational irrational integer whole number integer rational

  16. Square roots are written with a radical symbol . The number or expression inside a radical symbol is called the radicand. radicand radical symbol

  17. A square root is one of two equal factors of a number. 3  3 = 9 The positive square root of 9 is 3. -3  -3 = 9 The negative square root of 9 is -3.

  18. The positive square root of 4 is 2. The negative square root of 4 is -2. The positive square root of 225 is 15. The negative square root of 225 is -15. Zero has only one square root! The positive square root of is . The negative square root of is .

  19. Some square roots aren’t whole numbers. The square roots of numbers that aren’t perfect squares are IRRATIONAL numbers. In the case of irrational numbers, approximate the square root by rounding the result to two decimal places and replacing the equal sign with a sign. Approximate the square roots of:

  20. Negative real numbers do not have square roots because two negative numbers multiplied produce a positive number. = undefined The square root of a negative radicand is undefined! Evaluate each expression: 6 -6 undefined

  21. To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line. The number that corresponds to a point on a number line is called the coordinate of that point. • • • -5 -4 -3 -2-1 0 1 2 3 4

  22. Graph – 4, , – 6 and 0 on a number line. Order the numbers from least to greatest. • • • • -6 -5 -4-3 -2 -1 0 1 2 is an irrational number. Find its approximation on your calculator, then place it on the number line. – 6, – 4, 0,

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