Real Numbers: Number Systems Objective: Classify numbers by their subsets and organize numbers on a number line.

Do Now: What is a real number? Give me an example.

Real Numbers: Real numbers are numbers that are not imaginary. These numbers can be grouped into two major classifications: rational and irrational. Rational numbers: A real number that can be written as a ratio of two integers. Irrational numbers: A real number that cannot be written as a ratio of two numbers. Imaginary Numbers: A number that when squared gives a negative number.

Rational numbers include integers, whole numbers, and, natural numbers.

Natural Numbers {1,2,3,4,…} These are also known as counting numbers. These are the numbers you use when counting. No zero No decimals No fractions No negative numbers

Whole Numbers {0,1,2,3,…} Whole numbers are like counting numbers but you start at 0. No decimals No fractions No negative numbers

Integers {…,-2,-1,0,1,2,…} Integers are the counting numbers, zero, and the negative of the counting numbers. No decimals No fractions

The Real Number System Real Numbers Rational Numbers Irrational Numbers 3 1/4 -2 15% 2/3 1.456 -0.8 10 2 7 2 3 5

Real Numbers Rational Numbers Irrational Numbers 3 1/4 -2 1.5 2/3 1.456 -0.8 10 2 7 2 3 5 Integers Whole

Real Numbers Rational Numbers Irrational Numbers 3 1/4 -2 15% 2/3 1.456 -0.8 10 2 7 2 3 5 Integers Whole Like a Family Tree Natural

Real Numbers Notice there are still some more numbers to be classified. Before we can go into rational and irrational numbers, let’s go over: Absolute Values Perfect Squares Perfect Cubes Radicals Decimals Fractions

Absolute Values: An absolute value is how far a number is from zero. An absolute value is always positive.

Perfect Squares: A number created by squaring a whole number. Let’s go through some perfect squares. 1^2 to 15^2

Perfect Cubes: A number created by cubing a whole number. Let’s go through some perfect cubes.

Radicals: To take a square root of a number. The inverse operation of squaring. In order for a radical to exist in the real number system, the number under the square root or radical symbol, √ , must be positive.

Decimals: A number that has a decimal point followed by digits that show a value smaller than one. Types of Decimals: Repeating Non-repeating, Non-terminating Terminating

Fractions A fraction is a part of a whole. Types of fractions: Numerator: the top number that tells you how many parts you have. Denominator: the bottom number that tells you how many parts the whole is divided by. Types of fractions: Proper fraction: numerator < denominator (i.e. ¼) Improper fraction: numerator > denominator (i.e. 5/3) Improper fractions can be written as mixed numbers (i.e. 3/2  1 ½)

Number Line: All these different number classifications can be plotted on a number line.

Practice Place the sets on numbers on the number line. Set 1: 3 1/3 -0.6 11/4 √23 |5.7| 3.4 Set 2: 5/6 2.8 -5 |-5/4| -3.453 -√8

Independent Work: What are the two main categories real numbers are classified as? Classify the following numbers. Then, place the following numbers on the number line below. 9/4, -2.7, √2, |-4.5|, 5

Exit Ticket Based on what you have learned in class, what do you think are the key concepts from the lesson?