chapter 5 decimal notation slide 2copyright 2012, 2008, 2004, 2000 pearson education, inc....

CHAPTER

5Decimal Notation

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.1 Decimal Notation, Order, and Rounding5.2 Addition and Subtraction of Decimals5.3 Multiplication of Decimals5.4 Division of Decimals5.5 Using Fraction Notation with Decimal Notation5.6 Estimating5.7 Solving Equations5.8 Applications and Problem Solving

OBJECTIVES

5.5 Using Fraction Notation with Decimal Notation


a Use division to convert fraction notation to decimal notation.

b Round numbers named by repeating decimals.c Convert certain fractions to decimal notation by using

equivalent fractions.d Simplify expressions that contain both fraction and

decimal notation.




Now that we know how to divide using decimal notation, we can express any fraction as a decimal. This means that any rational number (ratio of integers) can be written as a decimal.

EXAMPLE



1





When division with decimals ends, or terminates ,the result is called a terminating decimal. If the division does not terminate, the result will be a repeating decimal.

EXAMPLE



3


EXAMPLE



3


Since 2 keeps reappearing as a remainder, the digits repeat and will continue to do so; therefore,

When there is a repeating pattern, the dots are often replaced by a bar to indicate the repeating part, in this case, only the 3.

Title



For a fraction in simplified form,• if the denominator has a prime factor other than 2 or 5, the decimal notation repeats.• if the denominator has no prime factor other than 2 or 5, the decimal notation terminates.

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5


Because 7 is not a product of 2’s and/or 5’s, we expect a repeating decimal.

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5



b Round numbers named by repeating decimals.


In applied problems, repeating decimals are rounded to get approximate answers. To round a repeating decimal, we can extend the decimal notation at least one place past the rounding digit and then round as before.

EXAMPLE




Round each to the nearest tenth, hundredth, and thousandth.

EXAMPLE



9 Gas Mileage.


A car travels 457 mi on 16.4 gal of gasoline. The ratio of number of miles driven to amount of gasoline used is gas mileage. Find the gas mileage and convert the ratio to decimal notation rounded to the nearest tenth.


c Convert certain fractions to decimal notation by usingequivalent fractions.


When a denominator is a factor of 10, 100, and so on, we can convert to decimal notation by finding (perhaps mentally) an equivalent fraction in which the denominator is a power of 10.

EXAMPLE



10


EXAMPLE



12



d Simplify expressions that contain both fraction anddecimal notation.


In certain kinds of calculations, fraction and decimal notation might occur together. In such cases, there are at least three ways in which we can proceed.

EXAMPLE



13


Perhaps the quickest method is to treat 0.576 as

EXAMPLE



13


A second way to do this calculation is to convert the fraction notation to decimal notation so that both numbers are in decimal notation.

EXAMPLE



13


A third method is to convert the decimal notation to fraction notation so that both numbers are in fraction notation.

EXAMPLE



13


EXAMPLE



14 Boating.


A triangular sail from a single-sail day cruiser is 3.4 m wide and 4.2 m tall. Find the area of the sail.

EXAMPLE



14 Boating.


1. Familiarize. We make a drawing and recall that the formula for thearea, A, of a triangle with base b and height h is

EXAMPLE



14 Boating.


2. Translate. 3. Solve.

EXAMPLE



14 Boating.


4. Check. To check, we repeat the calculations using the commutative law.

5. State. The area of the sail is 7.14 m2(square meters).

Our answer checks.

chapter 5 decimal notation slide 2copyright 2012, 2008, 2004, 2000 pearson education, inc....

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