Algebra Tutorials! Tuesday 30th of May Home Scientific Notation Notation and Symbols Linear Equations and Inequalities in One Variable Graphing Equations in Three Variables What the Standard Form of a Quadratic can tell you about the graph Simplifying Radical Expressions Containing One Term Adding and Subtracting Fractions Multiplying Radical Expressions Adding and Subtracting Fractions Multiplying and Dividing With Square Roots Graphing Linear Inequalities Absolute Value Function Real Numbers and the Real Line Monomial Factors Raising an Exponential Expression to a Power Rational Exponents Multiplying Two Fractions Whose Numerators Are Both 1 Multiplying Rational Expressions Building Up the Denominator Adding and Subtracting Decimals Solving Quadratic Equations Scientific Notation Like Radical Terms Graphing Parabolas Subtracting Reverses Solving Linear Equations Dividing Rational Expressions Complex Numbers Solving Linear Inequalities Working with Fractions Graphing Linear Equations Simplifying Expressions That Contain Negative Exponents Rationalizing the Denominator Decimals Estimating Sums and Differences of Mixed Numbers Algebraic Fractions Simplifying Rational Expressions Linear Equations Dividing Complex Numbers Simplifying Square Roots That Contain Variables Simplifying Radicals Involving Variables Compound Inequalities Factoring Special Quadratic Polynomials Simplifying Complex Fractions Rules for Exponents Finding Logarithms Multiplying Polynomials Using Coordinates to Find Slope Variables and Expressions Dividing Radicals Using Proportions and Cross Solving Equations with Radicals and Exponents Natural Logs The Addition Method Equations
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# Real Numbers and the Real Line

Real numbers can be represented by a coordinate system called the real line or x-axis. The real number corresponding to a point on the real line is the coordinate of the point. As the figure below shows, it is customary to identify those points whose coordinates are integers. The point on the real line corresponding to zero is the origin and is denoted by 0. The positive direction (to the right) is denoted by an arrowhead and is the direction of increasing values of x. Numbers to the right of the origin are positive. Numbers to the left of the origin are negative. The term nonnegative describes a number that is positive or zero. The term nonpositive describes a number that is negative or zero. Each point on the real line corresponds to one and only one real number, and each real number corresponds to one and only one point on the real line. This type of relationship is called a one-to-one-correspondence.

Each of the four points in the figure below corresponds to a rational numberâ€”one that can be expressed as the ratio of two integers. (Note that and .) Rational numbers can be represented either by terminating decimals such as or by repeating decimals such as  Real numbers that are not rational are irrational. Irrational numbers cannot be represented as terminating or repeating decimals. In computations, irrational numbers are represented by decimal approximations. Here are three familiar examples. See figure below. 