Converting between Percents, Decimals, and Fractions

Section. PRE-ACTIVITY PREPARATION Converting between Percents, Decimals, and Fractions Think about how often you have heard, read, or used the term percent (%) in its many everyday applications: The sales tax in Michigan is 6%. A % gratuity will be automatically added for parties of six or more. Hurry in! End-of-season clearance! 80% savings on all redticketed items! Full-time student enrollment increased this year by 2. percent. Last season our quarterback had a pass completion rate of 6.9 %. My score on the English quiz? 8%. You might use an equivalent fraction or decimal number instead of the percent in each example: The sales tax in Michigan is /0 (or 0.06). A gratuity of / (or 0.) will be automatically added for parties of six or more. Hurry in! End-of-season clearance! 4/ (or 0.80) savings on all red-ticketed items! Full-time student enrollment increased this year by /400 (or 0.02). Last season our quarterback had a pass completion rate of 289/467 (or 0.69). My score on the English quiz? 7/ (or 0.8). However, the percent is probably the most familiar and effective way to communicate the numbers. In this section, you will learn what the term percent represents. You will also learn the practical skill of converting between fractions, decimals, and percents, so that you can choose the appropriate form for presenting specific information. LEARNING OBJECTIVES Master the mathematical language of percents. Convert between equivalent decimals, fractions, and percents. Order a mixed set of fractions, decimals, and percents. 4

44 Chapter Percents TERMINOLOGY PREVIOUSLY USED build up convert factor order ratio reduce simple fraction NEW TERMS TO LEARN decimal fraction non-terminating repeating decimal percent percent number percent sign (%) terminating decimal BUILDING MATHEMATICAL LANGUAGE A decimal fraction is a simple fraction with a whole number numerator and a denominator of 0 or or 0, and so on. You can write any decimal number as a decimal fraction by first translating into words, then writing the fraction from the words. For example, the decimal number 0.0 is thirty-five thousandths, or as a decimal fraction. 0 A percent is a special type of ratio, comparing any number in the numerator to in the denominator. The numerator is referred to as the percent number. The percent sign (%) means per. For example, by the definition of percent, 22 = 22% "twenty-two percent" 22 is the percent number. = % "one hundred percent" is the percent number. 98 =98% "one hundred ninety-eight percent" 98 is the percent number. 2 2 = 2 % or 2.% "twelve and one-half percent" 2 is the percent number. 2 2 07. 7 = 07.% or % "seven tenths percent" 0.7 is the percent number. 0 or "seven tenths of a percent"

Section. Converting between Percents, Decimals, and Fractions 4 When the percent number is less than, as in ¼ %,.02%, or.82%, the percent is between 0% and %. When the percent number is greater than, but not a whole number, the percent is between two whole number percents. For example: ¼ % is greater than % and less than 4%. 6.% is halfway between 6% and 7%. You can use decimals, fractions, and percents interchangeably. To present information, you can choose the form that will convey the information most effectively. On the other hand, when you solve problems involving percents, you cannot calculate using a number in its percent form. Your only options are to use its fraction equivalent or its decimal equivalent. (Even a calculator with a % key converts the percent to its decimal form when that key is used.) Converting between the Decimal, Fraction, and Percent Form of a Number TECHNIQUES The following six techniques demonstrate how you can convert any decimal number, fraction, or percent to one of its other two equivalent forms. The six conversions are: Decimal Number to a Fraction Decimal Number to a Percent Fraction to a Percent Fraction to a Decimal Number Percent to a Decimal Number Percent to a Fraction Converting a Decimal Number to a Fraction Technique Write the decimal number as a decimal fraction and reduce the fraction to lowest terms. Models Convert the following decimals to their equivalent fractions or mixed numbers. Reduce fractions to lowest terms. A 0.022 B 4.48 22 0. 022 = 448. = 4 48 0 22 2 0 2 = 00 Answer 4 48 4 4 = 4 2 2 Answer

46 Chapter Percents Converting a Fraction to a Decimal Number Technique Divide the numerator of the fraction by its denominator. Special Case: The fraction is already (or can be built up to) a decimal fraction (see page 47, Model 2)??? Why do you do this? In its broadest sense, a fraction represents the quotient of two quantities. The division process will always result in a decimal number. When you divide a whole number by another whole number, the quotient will always be either a terminating decimal or a non-terminating repeating decimal. Terminating Decimal A terminating decimal is one for which there is a zero remainder at some point in the long division process. For example, if you divide by 8, the result will be.7, a terminating decimal. 0. 7 8. 000 ) 24 60 6 40 40 0 Non-terminating Repeating Decimal When the division results in a digit or in a sequence of digits that repeats, the quotient is a non-terminating repeating decimal. For example, when you divide 6 by, the result is... The notation for this is., with the bar over the indicating that it is the digit that repeats..... 6. 000 ) 0 9 0 9 0 9 To indicate a sequence of digits that repeats, use a bar over the sequence. For example, the result of dividing 4 by is.272727... or 27.. Model A Convert the following fractions and mixed numbers to decimals. Round to the ten-thousandth place for non-terminating decimals. 8 Divide by 8. The quotient is a terminating decimal. = 0.62 Answer 8 0. 62 8. 000 ) 48 6 40 40 0

Section. Converting between Percents, Decimals, and Fractions 47 B 6 6 = + The whole number does not change. 6 Convert the fraction 6 to a decimal. The quotient is a terminating decimal. =.062 Answer 6 0. 062 6. 0000 ) 96 40 2 80 80 0 C 2 0. 4666 2. 00000 ) 48 2 80 72 80 72 80 72 8 The quotient is a non-terminating repeating decimal. Rounded to the nearest ten-thousandth, 0.467 Answer 2 Model 2 Special Case: The Fraction is Already (or Can be Built Up to) a Decimal Fraction Convert the following to decimals. A 9 0 If the fraction is already a decimal fraction, or can easily be built up to a decimal fraction, simply write it in standard decimal notation. It is not necessary to divide. THINK 9 0 is nine tenths or 0.9 Answer B 8 4 2 8 4 4 8 6 2 4 = THINK eight and sixteen hundredths 8.6 Answer

48 Chapter Percents Converting a Decimal Number to a Percent Technique Multiply the decimal by %. That is, move the decimal point two places to the right and attach the percent sign (%).??? Why can you do this? Starting with a decimal number, for example 0.28, the Technique says that 0.28 % = 28.%. The Identity Property of Multiplication states that multiplying any number by does not change the value of the number. For this Technique, multiplying by % is multiplying by : % means and, from your knowledge of fractions, That is why the value of 0.28 does not change. Only its form changes. Now consider the second part of the Technique. Why is it that, to multiply by %, you can simply move the decimal point two places to the right and add a percent sign? Think about the process this way: 0.28 % = 28.% =. THINK The shortcut for multiplying by is to move the decimal point two places to the right. Models Convert the following decimals to their equivalent percents. A 0.822 0.822 % = 82.2% OR 0.822% = 82.2% Answer B.72.72 % = 72.% OR.72% = 72.% Answer

Section. Converting between Percents, Decimals, and Fractions 49 C D 0.04 0.04% = 4% Answer 0.009 0.009% = 0.9% Answer E 4 4.00% = 400% Answer Converting a Percent to a Decimal Number Technique Drop the percent sign and divide the percent number by. That is, drop the percent sign (%) and move the decimal point two places to the left. Special Case: The percent number contains a fraction (see page 460, Model 2)??? Why can do you do this? This Technique goes back to the definition of a percent as the ratio of the percent number to. 28. For example, 28.% = = 28. or 0.28 THINK The shortcut for dividing by is to move the decimal point two places to the left. Model A B Convert the following percents to their equivalent decimals. 8.4% 8.4% = 8.4 = 0.84 OR 8.4% = 0.84 Answer 28% 28% = 28 = 2.8 OR 28% = 2.8 Answer C D 2.% 2.% = 02.% 0.02 Answer Zero place digit needed. 0.7% 0.7% = 00.7% 0.007 Answer Two zero place digits needed.

460 Chapter Percents Model 2 Special Case: The Percent Number Contains a Fraction Convert each percent to its equivalent decimal. Round to the nearest ten-thousandths place, if necessary. A 62 4 % When the conversion is from a percent to a decimal, and the percent number contains a fraction, rewrite the fractional portion of the percent as a decimal. 4 = 4 = 0. 2 so 62 % = 62.2% = 0.622 Answer 4 B 4 % = = 0. 0. 4 % 4.% 4.% = 0.4 Answer Before looking at the remaining two techniques for converting between fractions and percents, think about the first four conversion techniques, as summarized in the table below. Fraction Decimal Percent 40 0. 2 40. 000 ) 80 0 0 0 0.2 and 0.2 % 2.% 40 reduce 2 0 0.2 and 0.2 2. 2.% Notice that the decimal form is the connecting conversion between fraction and percent, and between percent and fraction in the opposite direction. This bridge is the basis for the final two conversion techniques.

Section. Converting between Percents, Decimals, and Fractions 46 Converting a Fraction or a Mixed Number to a Percent Technique Step Convert the fraction or mixed number to a decimal. Step 2 Convert the decimal to a percent. Special Case: The denominator is (see below, Model 2) Special Case: The denominator is a factor of (see page 462, Model ) Special Case: The result of Step is a repeating decimal (see page 462, Model 4) Model A Convert the following to percents. 7 8 Step Step 2 7 8 = 0. 87 0.87% = 87.% Answer 0. 87 8 7. 000 ) 64 60 6 40 40 0 B 2 2 Step Step 2 2 2 = 2. 2.0% = % Answer 0. 2 0. ) 0 0 Model 2 Special Case: The Denominator of the Fraction is Convert to a percent: 7 If the denominator of the fraction is, the numerator IS the percent number. 7 = 7% Answer

462 Chapter Percents Model Special Case: The Denominator is a Factor of Convert to a percent: 9 9 Step Step 2 = 04. 0.4% = 4% Answer 04. 9. 00 ) 80 0 If the denominator of the fraction is a factor of, instead of dividing to determine the decimal, build the fraction to have as its denominator. The numerator will be the percent number. 9 9 4 = = = 4% by the definition of a percent. Model 4 Special Case: The Result of Step is a Repeating Decimal Convert the fraction to a percent. 6 Round to the nearest hundredth percent, if necessary. Step Step 2 6 0. 8 0. 8 6). 00000 48 8 8 8 8 2 0.8% = 8.% Answer If the directions say to round the percent to the nearest hundredth percent, round the decimal to the ten-thousandth place in the decimal form so that there will be two decimal places in the percent form to indicate accuracy to the hundredth percent place. Note: If the directions do not specify a rounding place, one option is to present the repeating decimal part using the bar notation. That is, = 8.% 6 Another is to present the repeating decimal part as a fraction. 2 = 08. 6 That is, 6 8 08. = % 6). 00 48 8 2

Section. Converting between Percents, Decimals, and Fractions 46 Converting a Percent to a Fraction or Mixed Number Technique Step Convert the percent to its equivalent decimal. Step 2 Convert the decimal to its equivalent fraction or mixed number and reduce. Special Case: The percent number is a whole number (see below, Model 2) Special Case: The percent number contains a fraction (see page 464, Model ) Model Convert the following to fractions or mixed numbers. Reduce the fractions to lowest terms. A 0.06% Step 00.06% = 0.0006 Step 2 6 6 2 0. 0006 = = 0, 000 0, 000 2 = 000 Answer B.2% Step 0.2% = 0.02 Step 2 2 2 4 8 2 0. 02 = =, 000, 000 4 = 2 = 4 2 Answer Model 2 Special Case: The Percent Number is a Whole Number Convert the following to fractions or mixed numbers. Reduce the fractions to lowest terms. A 4% 4 2 4% = 0. 4 = 2 = 27 0 Answer When the percent number is a whole number, there is no advantage to using its decimal equivalent. Simply write the percent number over (definition of percent) and reduce. 4 2 4% = 2 = 27 0 Answer B 2% 2 2 % = = 2 = 2 Answer

464 Chapter Percents Model Special case: The Percent Number Contains a Fraction Convert the following to fractions. Reduce to lowest terms. A 2 6 % When the percent number contains a fraction, drop the percent sign and multiply the percent number by / (same as dividing the percent number by ). Reduce the fraction. Note: This procedure assures that the resulting fractions will be the exact equivalent of the percent. 2 2 6 6 % = 2 9 = 6 = 6 = 9 600 Answer (reduced fully) B 2 2 % 2 2 % = = = 2 2 2 40 Answer Note: Since the ½ in the percent number can be converted to a terminating decimal, 0., you can choose to work through the decimal and convert as follows: 2 2 2 % = 02. % = 0. 02 = = 2 0 2 40 C % % = = = Answer

Section. Converting between Percents, Decimals, and Fractions 46 Validating Conversions In general, unless you rounded a decimal in the process, you can validate your answer by converting it back to the original form. Following are examples of validation for each of the six conversion techniques. Example : Decimal to Fraction Conversion: Validation: 0.22 = 0 Answer 0.22 (Convert to a decimal) 0). 00 0 0 Example 2: Fraction to Decimal A. Conversion: 8 = 0. 62 Answer Validation: (Convert 0.62 to a fraction) 62 2 0.62 = = 0 2 2 40 = 8 B. Conversion: Validation: 2 0. 47 Answer (rounded) Since 0.47 is rounded, it is not possible to convert it back to the exact original fraction. You can however, validate the equality of the decimal fraction form of your answer and the original fraction. The cross-products will be close but not exact because of the rounded decimal. 47? = 0 2? 47 2 = 0 004 000 Example : Decimal to Percent Conversion:.72 = 72.% Answer Validation: (Convert 72.% to a decimal.) 72.% =.72 continues on the next page

466 Chapter Percents Example 4: Percent to Decimal A. Conversion: 2.% = 0.02 Answer Validation: (Convert 0.02 to a percent) 0.02% = 2.% B. Conversion: Validation: 62 4 % = 0. 622 Answer (Convert 0.622 to a percent) 0. 622% = 62. 2% = 62 2 % = 62 4 % Example : Fraction to Percent A. Conversion: Validation: 9 = 4% Answer (Convert 4% to a fraction) 4 4% = 0. 4 = = 9 B. Conversion: Validation: 8 6. % (rounded) Change the rounded 8.% to its decimal equivalent. Then validate the equality of the decimal fraction and the original fraction. 8. % = 0. 8 8,? = 0, 000 6? 8, 6 = 0, 000 49, 998 0, 000 Example 6: Percent to Fraction Conversion: Validation: 0.6% = 00 Answer (Convert 00 to a percent.) 0. 006 00. 000 ) 000 0 0. 006% = 0.6%

Section. Converting between Percents, Decimals, and Fractions 467 How Estimation/Prediction Can Help As a mental math check to assure that your conversion answer is reasonable, keep the following comparison chart in mind. Fraction form Decimal form Percent form proper fraction (< ) 2 Example: improper fraction or mixed number (> ) <.0 Example: 0.4 >.0 < % Example: 40% > % Example: 4 Example:.7 Example: 7% Example: Convert 0.22 to a fraction. Prediction: THINK Since 0.22 <, the fraction will be proper (< ). Actual answer: 0 7 Example: Convert to a percent. 8 7 Prediction: THINK Since <, the percent will be < %. 8 Actual answer: 87.% Example: Convert.6 to a percent. Prediction: THINK Since.6 >.0, the percent will be > %. Actual answer: 60% You can, in fact, refine your predictions even more so; the following chart presents just a few of the comparisons you can use to predict or estimate your answer. Fraction form Decimal form Percent form < 2 < 0 > 2 > 4 < 0. < 0% < 0. < 0% > 0. > 0% > 0.7 > 7% > 2 > 2.0 > 0%

468 Chapter Percents Example: Convert 0.22 to a fraction. Prediction: THINK Since 0.22 < 0., the fraction will be < ½. Actual answer: 0 < 2 or 2 0 Example: 7 Convert to a percent. 8 Prediction: THINK Since 7 >, the percent will be 8 6 4 8 > 7% Actual answer: 87.% Example: Convert 2.8 to a percent. Prediction: THINK Since 2.8 > 2.0, the percent will be > 0% and since 2.8 > 2., the percent will be > %. Actual answer: 280% Example: Convert 240% to a fraction. Prediction: THINK Since 240% > 0%, the fraction will be a mixed number > 2 and Since 40% < 0%, the fraction part of the mixed number will be Actual answer: 2 2 < 2. Example: Prediction: Convert 0.07 to a fraction. THINK Since 0.07 < 0., the fraction will be < 0. Actual answer: 7 < 0 or 0 Example: Convert 0.07 to a percent. Prediction: THINK Since 0.07 < 0., the percent will be < 0%. Actual answer: 7%

Section. Converting between Percents, Decimals, and Fractions 469 Ordering a Mixed Set of Decimals, Fractions, and Percents You know how to order a set of decimal numbers (see Chapter 2) and a set of fractions (see Chapter ). Now with your knowledge of percents and of how all three forms are interchangeable, you can order a mixed set of decimals, fractions, and percents. Since the process of converting from percents to decimals and from fractions to decimals is simple, using the decimal forms for comparison is usually most efficient. TECHNIQUE Ordering a Mixed Set of Decimals, Fractions, and Percents Technique Step Convert all numbers to the same equivalent form. Step 2 Order them as you would for your chosen form. Model A List the following in order of their values, from lowest to highest:, 0., % 9 0. 9. 000 ) 9 0 9 0 9 Step : Write as decimals. 9 = 0. 0. Step 2: Order the decimals using trailing zeros. Rank 0. 2 0. is in decimal form 0. % = 0. 0.0 Answer : %, 9, 0. B List the following in order of their values, from lowest to highest: 07., %, 7. % 4 Step 2: Order the decimals Step : Write as decimals. Rank using trailing zeros. 0.7 = 0.7 0.700 4 % = 00.7% = 0. 007 0.007 7.% = 07.% 0.070 2 Answer : %, 7.%, 0.7 4

470 Chapter Percents ADDRESSING COMMON ERRORS Issue Incorrect Process Resolution Correct Process Losing track of the percent sign (%) while converting a percent that contains a decimal or fraction Convert to a Converting the fraction Convert decimal. % in the percent number to decimal. % to a a decimal or the decimal in the percent number to 06. a fraction only changes 0 ). the form of the percent % = 6. % 0 number. 0. 6% = 0.06 0 Drop the percent sign (%) only when you divide the percent number by. Convert 2.% to a fraction. Convert 2.% to a fraction. 2. % = 2 Answer: 2 7 7 2. % = 0. 02 2 = 0, 000 = 47 2, 000 Making an error in the shift of the decimal point when converting between decimals and percents Convert. to a percent.. = 0.0% 0 Convert 2.27% to a decimal. When converting from a decimal to a percent, the resulting percent number will always be times as large as the decimal number. When converting from a percent to a decimal, the resulting decimal number will always be times smaller than the percent number. Convert. to a percent. THINK. > so the percent will be greater than %. % = 0% Convert 2.27% to a decimal. 2.27% = 2272 Think about the decimal point shift in a conversion you know. 2 converts to 2% and THINK 2.27% < %, so the decimal will be less than. 2% converts to 0.2 0.2 2% 02.27% = 0.0227 Decimal Percent point shifts right Decimal Percent point shifts left

Section. Converting between Percents, Decimals, and Fractions 47 Issue Incorrect Process Resolution Correct Process Not presenting the required fraction form when converting from a percent to a fraction Convert 0.8% to a fraction. 08. 4 08. % = 0 4 Answer = 02. 2 First convert the percent to a decimal. Then write the decimal as a decimal fraction and reduce to lowest terms. The fraction equivalent of a decimal or percent should not contain a decimal point. It must be in the form of a simple fraction a whole number over a whole number. Convert 0.8% to a fraction. 0. 8% = 00. 8% = 0. 008 0. 008 = 2 = 2 8 0 Misinterpreting the denominator for the decimal fraction when converting from a decimal to a fraction Convert 0.2 to its fraction equivalent. 2 2 0. 2 = 0, 000 2 = = 80 400 80 Review Section 2. on how to read a decimal number. The place value of the last digit to the right of the decimal point determines the denominator for the decimal fraction. Convert 0.2 to its fraction equivalent. 2 2 0. 2 = = 0 2 8

472 Chapter Percents PREPARATION INVENTORY Before proceeding, you should have an understanding of each of the following: the terminology and notation associated with percents how to convert between fractions and decimals how to convert between percents and decimals how to convert between fractions and percents why you can apply a Technique without changing the value of the original number how, in general, to validate conversions how to order a mixed set of fractions, decimals, and percents

Section. ACTIVITY Converting between Percents, Decimals, and Fractions PERFORMANCE CRITERIA Converting between percents, decimals, and fractions accuracy required presentation of the answer Ordering a mixed set of percents, decimals, and fractions accurate conversions to the same form correct order CRITICAL THINKING QUESTIONS. When writing a decimal fraction for a given decimal number, how do you determine its denominator? Compare to the place value chart. Whatever is the place value of the digit farthest to the right, is the denominator of the fraction. 2. What are two ways to convert a fraction to decimal? For each procedure, when and why would you choose to use it? When the fraction is already (or can be built up to or down to) a decimal fraction, do so, then change to a decimal without doing any division. Divide the numerator by the denominator. In this case, you will get either a repeating or terminating decimal.. What are the two required characteristics of the final answer for a decimal to fraction conversion? The fraction must be left in simplest form as a proper fraction. OR If the answer is an improper fraction, leave the answer as a mixed number reduced to lowest terms. 47

474 Chapter Percents 4. Why does % = =? Percent means per hundred, so % = /. We already know that any number over itself is equal to one.. Why is a percent called a special type of ratio? A percent is a ratio of a number compared to, the % symbol is attached to show that the number is compared to, the % symbol takes up two decimal places, in order to use percent in computations it is necessary to convert from percent notation to decimal notation. Percent, meaning per hundred, means that numbers are compared per. Therefore, one can compare a number as either greater than or %, less than or %, or equal to or %. 6. What are four ways to convert fractions to percents? For each procedure, when and why would you choose to use it? Divide the denominator into the numerator. If the answer is a terminating decimal, move the decimal point two places to the right and append the % sign. When the answer to the fi rst method is a repeating decimal, move the decimal point two places to the right, then round to the proper place value, as stated in the directions, and append the % sign. If the denominator of the fraction is, the numerator is the percent number; then append the % sign. If the denominator can be built or reduced to, do so, then the answer is the numerator and append the % sign.

Section. Converting between Percents, Decimals, and Fractions 47 7. What are three possible ways to convert a percent to a fraction? For each procedure, when and why would you choose to use it?. If the percent is a whole number percent, you can quickly just put that number over and reduce. 2. If the percent is a decimal percent, move the decimal point two places to the left, then fi nd the appropriate place value and write that number over the place value amount and reduce your answer.. If the percent contains a fraction, change the fraction to an improper fraction, if necessary and multiply by / and reduce your answer. 8. How can you be sure that you have moved the decimal point in the proper direction when converting between decimals and percents? 2 (places) Remember to use the conversion steps: Fraction Decimal Percent. If you are changing from a decimal to a percent, move the decimal point two places to the right. If you are changing from a percent, move the decimal point two places to the left. 9. What does a decimal or a fraction within a percent mean? Since percents are portions of the base, the decimal with in a percent is a portion of a tenth of or hundredth of, etc. Also a fraction within the percent means that fractional part of.

476 Chapter Percents 0. How can you go about ordering a mixed set of fractions, decimals, and percents? Each case is dependant on the numbers involved, but it is usually easiest and requires the fewest steps to convert all of the numbers to decimals, compare the decimal equivalents, and then convert back to the original numbers. TIPS FOR SUCCESS Before you begin a conversion, identify what kind of number you have to start with (Fraction, Decimal, or Percent) and the kind of number you want to end with (F, D, or P). For most conversions, use decimals as a bridge between fractions and percents, as indicated in the individual rows of this chart. Fraction Decimal Percent Begin with a Fraction 4 0 2 0.7 7% Begin with a Decimal 0. 0% 2 4 0.2 Begin with a Percent 2% Use estimation/prediction to assure that your answer makes sense. Know some of the most common conversions: 0 2 = 0%, = 2%, = 0%, = 7%, = %, 66 2 % 4 2 4 =

Section. Converting between Percents, Decimals, and Fractions 477 DEMONSTRATE YOUR UNDERSTANDING. Convert each of the following to a simple fraction or mixed number. Reduce to lowest terms. Convert to a Fraction or Mixed Number Process Answer Validation (optional) a) 0.0 b) 0.6 00. = 0. 6 78 6 = 9 0 = 00 = 9 = 00. 0. 6 ) 9. 000 2 0 4 00 00 00 c) 8.42 842. = 8 42 8 2 = 0 8 2 0 8 2 2 = 8 42 0 2 = 842. 2. Convert each of the following to a decimal. Round to the nearest thousandth for non-terminating decimals. Convert to a Decimal Process Answer Validation (optional) a) 7 40 0.42 b) 00 0.002

478 Chapter Percents Convert to a Decimal Process Answer Validation (optional) c) 2 7 0.286 d).6 e) 4 4 4.8 f) 7 6 0.47

Section. Converting between Percents, Decimals, and Fractions 479. Convert each of the following to a percent. Convert to a Percent d 2 p Process Answer Validation (optional) a).2.2 = 2 or.2 = 2 2% 2% =.2 b) 0. 0. = 0 0% 0% =.0 c) 0.078 0.078 = 7.8 7.8% 7.8% =.078 d) 0.000 0.000 = 0.0 0.0% 0.0% = 0.000 e) = 00 00% 00% = f) 0.2 0.2 = 02 02% 02% = 0.2 4. Convert each of the following to a decimal. Round to the nearest ten-thousandth, if necessary. Convert to a Decimal Process Answer Validation (optional) a) 4% 4 =.4 0.4 0.4 = 4% b) 2.7% 2.7 =.027 0.027 0.027 = 2.7% c) 0.74% 0.74 =.0074 0.0074 0.0074 = 0.74% d) 82% 82 =.82.82.82 = 82% e) % =.0 0.0 0.0 = % f) 24 24½% = 24.% 24. =.24 0.24 2 % 0.24 = 24.% or 24½% g) 6 2 6.666% 6.666 =.0667 0.0667 0.666 = 6.66% % or 6 2 %

480 Chapter Percents. Convert each of the following to a percent. Round to the nearest hundredth percent, if necessary. Convert to a Percent Process Answer Validation (optional) a) 6 8.7% b) 7 0 4% c) 8 7.% d) 2 8.%

Section. Converting between Percents, Decimals, and Fractions 48 Convert to a Percent Process Answer Validation (optional) e) 4 7% f) 2 ½% 6. Convert each of the following to a simple fraction or mixed number. Reduce to lowest terms. Convert to a Fraction or Mixed Number Process Answer Validation (optional) a) 2% 4 b) 8% 9 0

482 Chapter Percents Convert to a Fraction or Mixed Number Process Answer Validation (optional) c) 6 2 % 7 60 d) 4 % 80 e) 0.74% 7 000 f) 0.8% 2 g) 62.% 8

Section. Converting between Percents, Decimals, and Fractions 48 7. Order the following from lowest to highest value:, 8%, 0. 4, 7% 8 8. Order the following from highest to lowest value:. %,, 0., 2 %, 2 6 TEAM EXERCISES Shade of one square. 0. In the grids below, fill in the correct number of rectangles to represent the following: a) 4% Use a pencil. Shade 4 squares. c) 40% Use a highlighter. Shade 40 squares. b) 0% Use a pen. Shade 0 squares. d) 0.6% Use a different color highlighter.

484 Chapter Percents 2. Fill in 7% of this grid. 7 n = 8. = n 0 2 Shade 8 squares. 2. What percent of this figure is unshaded? 2% + ½(2%)= 2% + 2.% = 7.% Answer: 7.% 4. Refer to the photograph of recyclable containers at right. Round each percent to the nearest tenth of a percent. a) What percent of the containers have a spray trigger? b) What percent of the containers are red? c) What percent of the containers are yellow? d) What percent of the containers are not yellow? a) 2 out of 4 containers b) out of 4 containers c) out of 4 containers = 4. % =. 7% = 2. 4% d) out of 4 containers = 78. 6%

Section. Converting between Percents, Decimals, and Fractions 48 IDENTIFY AND CORRECT THE ERRORS Identify the error(s) in the following worked solutions. If the worked solution is correct, write Correct in the second column. If the worked solution is incorrect, solve the problem correctly in the third column. Worked Solution What is Wrong Here? ) Write the equivalent fraction for 0.72%. Identify the Errors The fraction form should not contain a decimal point. Convert the percent to a decimal, then to a fraction. Reduce the fraction. Correct Process 00. 72% =. 0072 72 4 = 0 000 4 = 8, 2, 00 8 2 9 2, 00 2 =, Answer: 9, 2) Change.% to a fraction. Wrong place value used. ) Write.2% as a fraction. First, change to a decimal by moving the decimal point 2 places to the left. 4) Write 0.00 as a percent. CORRECT

486 Chapter Percents Worked Solution What is Wrong Here? Identify the Errors Correct Process ) Convert 7. to a percent. Move the decimal point 2 places to the right. D 2 P 6) Convert 2 to a percent. To change / to decimal, you must divde by.

Section. Converting between Percents, Decimals, and Fractions 487 ADDITIONAL EXERCISES Convert each of the following to a decimal. Round to the nearest ten-thousandth, if necessary.. 0.6. 4 4.62 8 2. 26%.26 6. 48% 0.48 4. 0.4444 7. 9 4. 2 8. 4 % 0.027 2 6 % 0.44 0.27 Convert each of the following to a percent. Round to the nearest hundredth percent, if necessary. 9. 0.2 2.%. 0.006 0.6% 0. 6.2% 4.. 2 44%. 2. 0.2 2% 6. 4.% 2% 60% Convert each of the following to a simple fraction or mixed number. Reduce to the lowest term. 7. 0.27 6 2. 4.8% 40 2 8. 2.6 2 22. 264% 2 6 2 9. 7.% 7 24 2. 96% 40 2. 4 % 2 24. % 2 400 Order the following from smallest to largest. 2. 26., 0. 62, 62. 9%, 8 4., 29, 8, 6 42.% 8, 6. 29%, 0. 62, 6 8 4 42 29,.,. %,