8/27/15 Please complete the “conclusion” questions on the back of your scavenger hunt. Share with a neighbor. Let’s share out.

Making Sense of Rational and Irrational Numbers Essential Question: How are rational and irrational numbers simplified?

Numbers can also be classified! Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko! Animal Reptile Lizard Gecko Numbers can also be classified!

It consists of 2 subsets – rational numbers and irrational numbers. The set of real numbers is all numbers that can be written on a number line. It consists of 2 subsets – rational numbers and irrational numbers. Irrational numbers Rational numbers Real Numbers Integers Whole numbers

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

Name all the sets of numbers to which the given number belongs. Circle the most specific set. Integer , Rational Rational Naturals , Whole , Integer , Rational Whole , Integer , Rational Rational

Venn Diagram Real Numbers Rational Integer Whole Natural

Remember… Rational numbers can be written as a fraction or… as either a terminating or repeating decimal. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

Classify the Following: Irrational -0.33333… Rational (equals -⅓)

Classify the Following: 0.818811888111… Irrational (no end, no repetition) 1⅔ Rational (can be 5/3 ) Rational (equals 10 or 10/1 )

Rational v. Irrational – How alike? Subsets of Real numbers Can be negative Can be non-terminating (never end)

Rational v. Irrational – How different? CAN be a fraction HAS a perfect square root Can be terminating or repeating decimals Irrational: CANNOT be a fraction Has NO perfect square root Can only be non-terminating, non-repeating decimals

Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as a fraction. 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 is irrational. A repeating decimal may not appear to repeat on a calculator, because calculators show a limited number of digits! Caution!

Identify each root as rational or irrational.

Decimal to Fraction: A skill you need for this unit! To change a decimal to a fraction, take the place value and simplify! 0.5 means “5 tenths,” so start with 5/10 Now simplify 5/10 to ½ So… 0.5 = ½

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

Rational Numbers CAN be made into a fraction a/b, where b ≠ 0. A repeating OR terminating decimal. 2/3 0.798798798…

Irrational Numbers CANNOT be made into a fraction a/b, where b ≠ 0. A non-repeating AND non-terminating decimal number. π 0.313311333111…