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

Biologists classify animals based on shared characteristics Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko. Rational Numbers are classified this way as well! You already know that some numbers can be classified as whole numbers, integers, or rational numbers. The number 2 is a whole number, an integer, and a rational number. It is also a real number. Animal Reptile Lizard Gecko

Venn Diagram: Naturals, Wholes, Integers, Rationals Real Numbers Rationals Integers Wholes Naturals

Name all the sets of numbers to which the given number belongs. Circle the most specific set. Integers , Rationals Rationals Naturals , Wholes , Integers , Rationals Wholes , Integers , Rationals Rationals

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!

Reminder Real numbers are all the positive, negative, fraction, and decimal numbers you have heard of. They are also called Rational Numbers. IRRATIONAL NUMBERS are usually decimals that do not terminate or repeat. They go on forever. Examples: π

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, take the place value and reduce! 0.5 means 5 tenths, so 5/10. Now reduce 5/10 = ½ 0.5 = 1/2

Converting Fractions and Decimals To change a fraction to a decimal, take the top divided by the bottom, or numerator divided by the denominator.

Complete the table. Fraction Decimal

Repeating Decimals Fraction Decimal Every rational number (fraction) either terminates or repeats when written as a decimal.

Repeating Decimals Fraction Decimal

Repeating Decimals Fraction Decimal

Thankyou We shall continue with representing Rational and Irrational Numbers on the Number Line in forthcoming sessions