ARC Instructional video MAT 120 College Algebra REAL NUMBERS ARC Instructional video MAT 120 College Algebra

Real Numbers Real Numbers are every number. Therefore, any number that you can find on the number line. Real Numbers have two categories. Real numbers are the numbers that we use every day.

Real Numbers REAL NUMBERS 154,769,852,354 1.333 -5,632.1010101256849765… -8     Here are a few examples. Some might not seem obvious , like the square root of 101 or pi, but all of these are real numbers.   61 π 49% 549.23789

Two Kinds of Real Numbers Rational Numbers Irrational Numbers Two categories of real numbers: Rational and Irrational.

Rational Numbers A rational number is a real number that can be written as a fraction. A rational number written in decimal form that is terminating or repeating.

Examples of Rational Numbers 16 1/2 3.56 -8 1.3333… - 3/4 For example: 16, one half, 3.56, or 1.3 repeating. Also negative numbers are

One of the subsets of rational numbers Integers One of the subsets of rational numbers

What are integers? Integers are the whole numbers and their opposites. Examples of integers are 6 -12 186 -934

Integers are rational numbers because they can be written as fraction with 1 as the denominator. Remember integers are rational because we can write them with a 1 underneath them.

Types of Integers Natural Numbers(N): Natural Numbers are counting numbers from 1,2,3,4,5,................ N = {1,2,3,4,5,................} Whole Numbers (W): Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,............... W = {0,1,2,3,4,5,..............} W = 0 + N There are 2 types of integers: Natural and Whole numbers. The only difference is that whole includes the number 0.

REAL NUMBERS NATURAL Numbers WHOLE Numbers IRRATIONAL Numbers INTEGERS Here is how the real number system is constructed. RATIONAL Numbers

Irrational Numbers An irrational number is a number that cannot be written as a fraction of two integers. Irrational numbers written as decimals are non-terminating and non-repeating.

Irrational numbers If a whole number is not a perfect square, then its square root is an irrational number. A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Caution!

Examples of Irrational Numbers   Pi π   Here are a few examples.

Try this! Here is some practice for you to try.

Answers to Previous Slide a) Irrational b) Irrational c) Rational d) Rational e) Irrational

A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all. Remember we cannot divide by zero so that is considered undefined.