# Numbers and Operations

## Overview

### Description

Numbers and operations are the foundations of algebra. There are many sets of numbers. The set of counting numbers is known as the natural numbers. This set includes other types of numbers. When zero is included, the set is called whole numbers. When negative numbers are included, the set is called integers. Quotients of integers make up the rational numbers, and the set of all fractions and decimals is called real numbers. Various forms of notation are used to represent numbers, including exponential, scientific, and radical notation. Operations performed on expressions include addition, subtraction, multiplication, division, exponents, and roots. When performing numerical operations, a specific order is used to ensure consistent answers.

### At A Glance

• Sets of numbers include natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
• Exponential notation can be used to represent repeated multiplication. Scientific notation uses exponents to represent very large or very small numbers.
• Rules of exponents can be used to simplify expressions containing exponents.
• Properties of radicals can be used to simplify radical expressions.
• A radical expression in simplest form has no perfect powers or fractions in the radicand and no fractions in the denominator of a fraction.
• Fractions with radicals in the denominator can be simplified by multiplying by a fraction equivalent to 1.
• Rational exponents can be used to represent radicals, or $n$th roots.
• Operations in an expression are performed in a specific order: operations within grouping symbols, exponents, multiplication and division from left to right, and addition and subtraction from left to right.