Rational and Irrational Numbers

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?

7

3

2

6.2533678

1 rational irrational

irrational rational

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.

-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

0

-7 280% 14/31 3/7

Order from least to greatest: -7, 1 3/7, 280%, 14/3

Do Example 1 NowExample 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

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