Free Algebra
Miscellaneous Equations
Operations with Fractions
Undefined Rational Expressions
Writing Equations for Lines Using Sequences
Intersections of Lines and Conics
Graphing Linear Equations
Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
The circle
Adding Polynomials
Adding Fractions with Unlike Denominators
Factoring Polynomials
Linear Equations
Powers of Ten
Straight Lines
Dividing With Fractions
Multiplication Property of Equality
Rationalizing Denominators
Multiplying And Dividing Fractions
Distance Between Points on a Number Line
Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
Imaginary Numbers
Values of Symbols for Which Fractions are Undefined
Graphing Equations in Three Variables
Writing Fractions as Decimals
Solving an Equation with Two Radical Terms
Solving Linear Systems of Equations by Elimination
Factoring Trinomials
Positive Rational Exponents
Adding and Subtracting Fractions
Negative Integer Exponents
Rise and Run
Multiplying Square Roots
Multiplying Polynomials
Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Factoring by Grouping
Extraneous Roots
Variables and Expressions
Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
Solving Linear Inequalities
Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions

Writing Fractions as Decimals

Objective Learn how to write fractions as decimals, using long division.

This lesson is an excellent application of long division and division of decimals. It is important to be able to write fractions as decimals. It is more difficult to compare and perform addition and subtraction on fractions than on decimals.

Fractions Represent Division

Remember that fractions really represent the division of one integer by another integer. For example, represents the division of 5 by 7.

Writing Decimals as Fractions

The division represented by a fraction can be performed to produce the decimal equivalent of the fraction.

Key Idea

To write a fraction in decimal form, divide the numerator by the denominator.

Example 1

Write each fraction as a decimal.


a. First write 3 as 3.0, and then divide by 5.

So, .

b. Write 1 as 1.0 and then divide by 2.

So, .

Sometimes it is necessary to add more than one zero at the end of the decimal created from the numerator. One additional zero is added and the division continues each time a division step results in a remainder. This is shown in the following examples.

Example 2

Write each fraction as a decimal.


a. When we try to write as a decimal, with 7 written as 7.0, we get

Since the division in this step resulted in a remainder of 10, we add another zero to the dividend, 7.0, and continue dividing.

The division has no remainder, so .

b. Begin by rewriting as the division 3.0 ÷ 25.

Since there is a remainder, add another zero and continue dividing.

So, .

The two previous examples show a pattern in which for single-digit denominators only one zero is needed for the division, and for double-digit denominators two zeros are needed. The following example shows that the pattern was only coincidental.

Example 3

Write as a decimal.


Write as the division 5.0 ÷ 8.

Add another zero to the dividend and continue dividing.

Add another zero and continue dividing.

So, .

Terminating and Repeating Decimals

Sometimes the division never comes out evenly no matter how many zeros we add.

Example 4

Write as a decimal.


Use long division as in Examples 1–3.

The remainder at each step will always be 1 and the next digit in the quotient will always be 3. So the quotient is 0.333… (the dots mean that the pattern continues indefinitely), which can also be written as (the bar over the 3 means that the digit repeats).

When the division never comes out evenly, the fraction cannot be written as a terminating decimal (a decimal that ends). However, in these situations there is always a pattern of digits that eventually repeats, and it may involve more than just a single digit, as in Example 4.

Expressions such as 0.33333… and 0.090909… are called repeating (or nonterminating ) decimals because one or more digits repeat.

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