Unit: Operations with Rational Numbers- Types of Numbers Video # 1 Learning Target: I can identify a real, rational, irrational, whole, or natural number.

How do we classify a number? Just like how you have a name that represents the family you belong to, numbers have different families that they belong to as well. All of the numbers you have learned about in the past are called real numbers. If a number is not a real number it is called an imaginary number. You will learn more about imaginary numbers in high school.

How do we classify real numbers? There are two major “families” in the real number system: Rational Irrational -A number that can be written as a fraction -A decimal that terminates or stops -A decimal that has a repeating pattern -”messy numbers” or “numbers that aren’t being rational” -A number that can NOT be written as a fraction -A decimal that goes on forever (does not end and does not repeat) Specific types of Rational #s Natural/Counting Numbers: 1, 2, 3, 4.. Whole Numbers: 0, 1, 2, 3, 4, …… Integers: …..-3, -2, -1, 0, 1, 2, 3, …. Examples: √13, π, 0.12345… Examples: ¾, 0.6666666, 1.25, √25, 0, 4, -20

Types of decimals There are two “families” of decimals: Terminating Non-Terminating Decimal that ends, stops, or “terminates” Terminating decimals are rational numbers Decimal that goes on forever: -Repeating: decimal that has a repeating pattern (rational) Non-repeating: decimal that has no pattern (irrational) Ex: 2.5, 54.625, ½ = 0.5 Ex: 4.12121212121212121212 (rational) 1/3 = 0.3333333333333 (rational) Π = 3.14159268… (irrational)

Example 1 Number Classification Classify the following as rational or irrational. If the number is rational, determine if it is natural, whole, or an integer. (Numbers might have several names). Number Classification 3 rational, natural, whole, integer π irrational √9 √3 -2 rational, integer 0.66666 rational

Example 2 Put the following numbers in order on the number line below. √13, -√16, -2, ½, 0.33, π, -2/3 ½ √13        π -2/3 0.33 -√16 -2