Explore the Lesson

C. Irrational Numbers and Number Lines

Placing Irrational Numbers on a number line helps to make sense of where they belong in relation to more familiar numbers. Estimation is one tool that can help with this process, but there are others that you will soon see.

 

Example 1

Place the following numbers on the number line provided and identify the Real Number subsets to which each belongs.


It is important to include the Real Numbers as a set to which each number covered in this course belongs.

Rational and Real
1.75 Rational and Real
Natural, Whole, Integer, Rational, and Real
-643=-4
 Integer, Rational, and Real
Irrational and Real

 

Converting mixed radicals to entire radicals is another method of comparing and ordering Irrational Numbers.

Example 2

Order the following Irrational Numbers from least to greatest.

Step 1: Convert all mixed radicals to entire radicals.

Step 2: Compare and order the radicand values from least to greatest.

Step 3: Order the original Irrational Numbers from least to greatest.

Using a calculator to determine the approximate value is another method to compare and order Irrational Numbers.

Example 3

Order the following numbers on the number line provided.