Irrationals, Integer Exponents and Scientific Notation Overview

Introduction

In this module, we will learn to distinguish between rational and irrational numbers using decimal expansion. We will learn to approximate irrational numbers and compare them on a number line. We will learn the properties of integer exponents as we simplify them to numerical expressions. We will also learn to identify perfect squares and perfect cubes and use them in equations. Finally, we will learn to write numbers in scientific notation and perform mathematical operations expressed in scientific notation.

Essential Questions

How do we know if numbers are rational or irrational?
How can we estimate where irrational numbers should be placed on the number line using rational approximations?
What are the properties of integer exponents?
How can we take the square root and the cube root of a number?
How can we use square roots and cube roots to solve equations?
What is scientific notation and how can we perform operations with its form?

Key Terms

The following key terms will help you understand the content in this module.

Rational Number – Any number that can be written as a fraction.

Irrational Number – A number that cannot be written as a fraction, terminating decimal or repeating decimal

Base – The number used as a factor when raised to a power.

Exponent – The number used to indicate how many times the base is used as a factor.

Power – A number produced by raising a number to an exponent.

Radical Symbol – The symbol used to represent the nonnegative square root of a number.

Root – The number used as a factor in radicals.

Index – The number above the radical symbol used to indicate the exponent used in the root

Principal Square root –The nonnegative square root of a number.

Perfect Square – The square of a whole number

Scientific Notation –A method of writing very large or very small numbers by using powers of 10.

Standard Notation – When a number is written using only number digits.

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