Real Numbers and the Number Line

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Presentation transcript:

Real Numbers and the Number Line The numbers in the pattern are integers and their squares.

Table of Perfect Squares Integer Perfect Square 1 2 3 4 5 6 7 8 9 10 Integer Perfect Square 11 12 13 14 15 16 17 18 19 20

Real Numbers and the Number Line A number a is a square root of a number b if a2 = b. Example: Together, the radical symbol and the radicand form a radical.

Problem 1 What is the simplified form of each expression?

Problem 2 Estimating a Square Root The square of an integer is called a perfect square. For example, 49 is a perfect square since When a radicand is not a perfect square, you can estimate the square root. Method 1: Estimate

Problem 2 Estimating a Square Root Method 2: Estimate

Classifying Real Numbers You can classify numbers using sets. A set is a well-defined collection of objects. Each object is called an element of the set. A subset of a set consists of elements from the larger set. You can list elements of a set within braces {}. The set of Real Numbers is the largest set of numbers that you will work with. It is divided into two subsets: the Rational Numbers and the Irrational Numbers.

The Real Numbers Rational Numbers Irrational Numbers Real Numbers

Rational Numbers The Rational Numbers have a subset called the integers. The integers are the set The Integers have a subset called the whole numbers. The Whole Numbers are the set

Rational Numbers The Whole Numbers have a subset called the natural numbers. The Natural Numbers are the set Some square roots are rational numbers and some are irrational numbers. If a whole number is not a perfect square, then its square root is irrational.

Classifying Real Numbers

Problem 3 Classifying Real Numbers To which subsets of the real numbers does each number belong to?

Inequality An inequality is a mathematical sentence that compares the values of two expressions using an inequality symbol. The inequality symbols are:

Problem 4 Comparing Real Numbers What is an inequality that compares the following two numbers?

Problem 5 Graphing and Ordering Real Numbers Order the following set of numbers from least to greatest. Note: To perform this task, you can write every number as a decimal rounded to the nearest hundredth, and then graph each of the numbers on a number line. Then, read the graph from left to right.