4.7 Converting from Decimals to Fractions

1 2001 McGraw-Hill CompaniesConverting from Decimals to a decimal to a common fractionUsing what we have learned about place values, you can easily write Decimals as commonfractions. The following rule is used. 379 Example 1 Converting a Decimal to a Common One placeOne zeroTwo placesTwo zerosThree placesThree zeros25710009100710 Step 1 Write the digits of the decimal without the decimal point. This will bethe numerator of the common 2 The denominator of the fraction is a 1 followed by as many zeros asthere are places in the by Step:To Convert a Terminating Decimal Less Than1 to a Common Fraction CHECK YOURSELF 1 Write as common Fractions .(a) (b) 2 When a decimal is converted to a common fraction, the common fraction that resultsshould be written in lowest a Decimal to a Common FractionConvert to a fraction and write the result in lowest 3951000 79200 CHECK YOURSELF 2 Write a common the numeratorand denominator by 2001 McGraw-Hill CompaniesExample 3 Converting a Decimal to a Mixed NumberWrite as a mixed 2771000, so 122771000 NOTER epeating Decimals canalso be written as commonfractions, although the processis more complicated.

2 We willlimit ourselves to theconversion of terminatingdecimals in this the decimal has a whole-number portion, write the digits to the right of the decimalpoint as a proper fraction and then form a mixed number for your YOURSELF 3 Write a mixed the sizes of common Fractions and Decimals requires finding the decimalequivalent of the common fraction and then comparing the resulting 4 Comparing the Sizes of Common Fractions and DecimalsWhich is larger, Write the decimal equivalent of That decimal is Now comparing and , we see that is the larger of the numbers: or YOURSELF 4 Which is larger, or YOURSELF ANSWERS1. (a) (b) 344331000 11403111000310; 2001 McGraw-Hill CompaniesExercisesWrite each of the following as a common fraction or mixed number. Write your answer inlowest each of the following statements, using the symbol or . _____ _____ _____ _____ Section Date 2001 McGraw-Hill following table gives the winning percentage for the teams in the AmericanLeague West.

3 What fraction of their games has each team won? , 69125, 247500, 83200 57252171006310116 59100017125381740295012255871000 following table gives the winning percentages of the top five coaches in NFLhistory. What fraction of his games has each coach won? Converting Fractions to DecimalsFind the decimal equivalent of to the nearest 24 Display(nearest hundredth)524 524 2001 McGraw-Hill CompaniesUsing Your Calculator toConvert Between Decimalsand FractionsA calculator is very useful in Converting common Fractions to Decimals . Just divide thenumerator by the denominator, and the decimal equivalent will be in the 1 Converting Fractions to DecimalsFind the decimal equivalent of 7 16 is the decimal equivalent of . YOURSELF 1 Find the decimal equivalent of .516 CHECK YOURSELF 2 Find the decimal equivalent of to the nearest , you will want to round the result in the 2To find the decimal equivalent of a mixed number, use the following calculators showthe 0 to the left of the decimalpoint and seven digits to theright.

4 Others omit the 0 andshow eight digits to the yours with this Mixed Numbers to DecimalsChange to a 8 7 758 2001 McGraw-Hill CompaniesExample 3 NOTET here are several waysto do this, depending on thecalculator you are using. Forexample,7 5 8will work on most scientificcalculators. Try it on yours. CHECK YOURSELF 3 Find the decimal equivalent of YOURSELF 4 Find the decimal equivalent of on the calculator you are using, the result may be rounded at its last 4 Converting Fractions to DecimalsFor :5 9 Displayor Rounded 59 CHECK YOURSELF or 2001 McGraw-Hill CompaniesCalculator ExercisesFind the decimal bar bar bar each decimal to a Section Date 2001 McGraw-Hill