1-3: Comparing and Ordering Rational and Irrational Numbers

Key Concept

All real numbers can be located on a number line. This means that all irrational numbers can be located on a number line. You can use a number line to graph and order real numbers.

A number line.

You can approximate π by comparing the circumference of a circle C to its diameter d.

A circle of circumference C = 18.85 in. and diameter d = 6 in. A number line with a point at 3.14.

Part 1

Example Comparing Rational and Irrational Numbers

Complete each statement using >, <, or =.

  • a.

  • b.

  • c.

  • d.

  • e.

  • f.

Solution

For each pair of values, draw a number line and approximate the placement of the irrational numbers.

  • a. A number line with a point at 1.0. radical 3 > 1. radical 3 = approximately 1.73: a point is plotted between 1.7 and 1.8, closer to 1.7.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties