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Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   
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Writing Decimals as Fractions

Objective Reinforce your understanding of the meaning of decimal notation as an equivalent form for fractions with a power of 10 in their denominator.

This lesson consists of reinforcement of students’ understanding of the decimal expansion. This is a good opportunity to correct any misunderstandings they may have about decimal expansion.

 

Decimal Notation

In a decimal, each digit to the right of the decimal point represents a fractional value with a denominator that is a power of 10 (10, 100, 1,000, …). For example, the value represented by the digit 2 in 0.256 is "two tenths". The values represented by the digits 5 and 6 are “five hundredths” and “six thousandths”, respectively. This means the decimal 0.256 can be represented by the sum .

 

Example 1

Represent 0.78 as the sum of fractions whose denominators are powers of 10.

Solution

0.78 is equivalent to the sum .

It is only the digits to the right of the decimal point that are represented by fractions in a decimal expansion. The digits to the left of the decimal point represent the whole-number part of the decimal.

Example 2

Write 3.56 as a sum involving fractions whose denominators are powers of 10.

Solution

3.56 can be represented by the sum .

 

Writing Decimals as Fractions

We can write the fractional parts of a decimal expansion as a single fraction by writing them using a common denominator.

Example 3

Write 0.256 as a single fraction.

Solution

As shown previously, we know that 0.256 =

The common denominator for these fractions is 1,000.

So, 0.256 is equivalent to the fraction .

Example 4

Write 3.56 as a single fraction.

Solution

In Example 2, it was shown that . Since , the common denominator is 100.

So, 3.56 is equivalent to .

Alternately, we could add just the fractions in the decimal expansion , and get a mixed number as our result.

So the decimal 3.56 is also equivalent to the mixed number .

Although it is easy to give a simple step-by-step procedure for writing a decimal as a fraction, it is important to do examples of the kind we have just done so that you can see why the procedure works.

 

Writing Decimals as Fractions

1. Count the number of digits to the right of the decimal point in the given decimal.

2. Drop the decimal point from the decimal, and place the resulting whole number in the numerator of the fraction.

3. In the denominator, write the power of 10 that has as many zeros as there were digits to the right of the decimal point in the given decimal.

 

Example 5

Write 0.638 as a fraction.

Solution

Step 1 The number of digits to the right of the decimal point is 3.

Step 2 Dropping the decimal point gives the whole number 638. Use this number as the numerator of the fraction.

Step 3 From Step 1, we know that the power of 10 used in the denominator should have 3 zeros. So 1,000 is the denominator of the fraction.

Example 6

Write 21.67 as a fraction and a mixed number.

Solution

Step 1 The number of digits to the right of the decimal point is 2.

Step 2 Dropping the decimal point gives the whole number 2,167. Use this number as the numerator of the fraction.

Step 3 The denominator of the fraction should be 100.

As a mixed number, .

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