Making Sense of Rational and Irrational Numbers

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Presentation transcript:

Making Sense of Rational and Irrational Numbers Objectives: Identify number sets. Write decimals as fractions. Write fractions as decimals.

The set of real numbers is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers. Irrational numbers Rational numbers Real Numbers Integers Whole numbers

Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

Rational Numbers Natural Numbers - Natural counting 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: -0.76, -6/13, 0.08, 2/3

Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Caution!

Identify each root as rational or irrational.

Decimal to Fraction: A skill you will need for this unit! To change a decimal to a fraction by dividing the denominator by the numerator 5/10= 5 ÷ 10 = 0.5

Complete the table. Fraction Decimal

Rational and Irrational Numbers Determine whether the following are rational or irrational. (a) 0.73 (b) (c) 0.666…. (d) 3.142 (e) rational irrational rational rational irrational (f) irrational

https://www.youtube.com/watch?v=RPVu3pYDUFI

RULES FOR ADDING AND MULTIPLYING RATIONAL AND IRRATIONAL NUMBERS Rule 1: Rational + Rational = Rational Example: Rule 2: Rational x Rational = Rational Example: Rule 3: Rational x Irrational = Irrational Example:

RULES FOR ADDING AND MULTIPLYING RATIONAL AND IRRATIONAL NUMBERS Rule 4: Irrational + Rational = Irrational Example: