Rational and Irrational Numbers Power point notes to accompany Lesson 1 Semester 2

Classifying Numbers Numbers can be classified For instance, we can pick out all of the numbers that are divisible by 2. They are classified as even numbers. We can also classify numbers in other ways.

Rational and Irrational Numbers can be classified as rational numbers. Rational numbers are numbers that in decimal form, are either terminating OR repeating.

Terminating numbers A terminating number is a number that terminates, which means ends. Examples of terminating numbers: 3.14 4.5678932221 0.33339 Examples of numbers that do NOT terminate (do not end) 3.333333… pi 0.121231234….

Repeating Numbers A repeating number is a number that does not terminate, but it repeats over and over EXACTLY THE SAME WAY Examples of repeating numbers: 3.33333…. 4.34343434…… Examples of NON-repeating numbers: 3.343453456….. pi 9.352109….

Rational vs. Irrational If a number repeats exactly, or terminates, then it is a rational number. If a real number is NOT rational, then it is irrational.

Rational or irrational?  1 irrational rational 1 3/7 is rational because it repeats as a decimal (1.42857142857142857) pi is irrational because it is non-repeating and non-terminating square root of 2 is irrational because it is non-repeating and non-terminating 6.2533678 is rational because it terminates 6.2533678 rational irrational

Real = Rational + Irrational Real Numbers Another classification of numbers is the set of numbers called Real Numbers. This one is easy. Real numbers are the rational numbers and the irrational numbers combined. Real = Rational + Irrational

Place the following numbers in order from least to greatest. -7, 14/3, 280%, 1 3/7 Step 1. Change into decimals. Step 2. Place on a number line.

Order from least to greatest: -7, 1 3/7, 280%, 14/3 -7 = -7.0 14/3 = 14 divided by 3  4.7 280% = 280 divided by 100  2.8 1 3/7 = 1 + 3/7  1.43 -7 14/3 1 3/7 280% Order from least to greatest: -7, 1 3/7, 280%, 14/3

Do Example 1 Now Example 1 Order numbers from least to greatest; place on number line: 5/6 4 ¼ 300% 0. 23 3/10 Step 1: Convert to decimals: 5/6 = ______ 4 ¼ = ______ 300% = ______ 0. 23 = ______ 3/10 = ______

Example 1 Step 1: Convert to decimals: 5/6 = 0.833 4 ¼ = 4.25 300% = 3.0 0. 23 = 0.23 3/10 = 0.3 Order from least to greatest: 0.23, 0.3, 0.833, 3.0, 4.25

0.23, 0.3, 0.833, 3.0, 4.25 0.23 0.833 3.0 0.3 4.25

Example 2 Which is smaller: -2 or -3 -3 is smaller Convert -3 ½ to decimal form -3 + - ½ = -3 + -0.5 = -3.5