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453

PRE-ACTIVITY

PREPARATION

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 15% gratuity will be automatically added for parties of six

or more.• Hurry in! End-of-season clearance! 80% savings on all red-

ticketed items!• Full-time student enrollment increased this year by 2.5

percent.• Last season our quarterback had a pass completion rate of

61.9 %.• My score on the English quiz? 85%.

You might use an equivalent fraction or decimal number instead of the percent in each example:• The sales tax in Michigan is 3/50 (or 0.06).• A gratuity of 3/20 (or 0.15) will be automatically added for parties of six or more.• Hurry in! End-of-season clearance! 4/5 (or 0.80) savings on all red-ticketed items!• Full-time student enrollment increased this year by 35/1400 (or 0.025).• Last season our quarterback had a pass completion rate of 289/467 (or 0.619).• My score on the English quiz? 17/20 (or 0.85).

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 specifi c information.

• Master the mathematical language of percents.• Convert between equivalent decimals, fractions, and percents.• Order a mixed set of fractions, decimals, and percents.

Converting between Percents,

Decimals, and Fractions

LLEARNINGEARNING OOBJECTIVESBJECTIVES

Section 5.1

454 Chapter 5 — Percents

TTERMINOLOGYERMINOLOGY

NEW TERMS TO LEARN

decimal fraction

non-terminating repeating decimal

percent

percent number

percent sign (%)

terminating decimal

PREVIOUSLY USED

build up

convert

factor

order

ratio

reduce

simple fraction

BBUILDING UILDING MMATHEMATICAL ATHEMATICAL LLANGUAGEANGUAGE

A decimal fraction is a simple fraction with a whole number numerator and a denominator of 10 or 100 or 1000, 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 0.035 is “thirty-five thousandths,” or

A percent is a special type of ratio, comparing any number in the numerator to 100 in the denominator. The numerator is referred to as the percent number.

The percent sign (%) means “per 100.” For example, by the definition of percent,

35

1000 as a decimal fraction.

22

10022= % "twenty-two percent" 22 is the percent number.

100

1100100= % "one hundred percent" 100 is the percent number.

198

100==198% "one hundred ninety-eight ppercent" 198 is the

or

percent number.

1212

10012

1

2= % "twelve and one-half percent" 112 5. % 22

1

2 is the

or %

percent number.

0 7

1000 7

7

10

.. %= "seven tenths percent" 0.7 is the percent number.

or "seven tenths of a percent"

455Section 5.1 — Converting between Percents, Decimals, and Fractions

When the percent number is less than 1, as in ¼ %, .02%, or .82%, the percent is between 0% and 1%.

When the percent number is greater than 1, but not a whole number, the percent is between two whole number percents. For example: 3¼ % is greater than 3% and less than 4%. 16.5% is halfway between 16% and 17%.

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.)

TTECHNIQUESECHNIQUES

Technique

Write the decimal number as a decimal fraction and reduce the fraction to lowest terms.

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

►►A 0.022 4.48►►B0 022

221000

22 21000 2

. =

÷÷= 11

500 Answer

4 48 448

100

448 4

100 4

. =

÷÷

= 41225

Answer

Models

Convert the following decimals to their equivalent fractions or mixed numbers. Reduce fractions to lowest terms.

Converting between the Decimal, Fraction, and Percent Form of a Number


Technique

Divide the numerator of the fraction by its denominator.

Converting a Fraction to a Decimal Number

Model 1

? ? ? 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.

)8 3 000

2 4

60

56

40

40

0

0 375..

−

−

−

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 3 by 8, the result will be .375, a terminating decimal.

)3 16 000

15

10

9

10

9

10

9

5 333..

−

−

−

−

....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 16 by 3, the result is 5.333...

The notation for this is , with the bar over the 3 indicating that it is the digit 3 that repeats.

5 3.

To indicate a sequence of digits that repeats, use a bar over the sequence. For example, the result of dividing 14 by 11 is 1.272727.... or 1 27. .

►►A

Convert the following fractions and mixed numbers to decimals. Round to the ten-thousandth place for non-terminating decimals.

58

Divide by .

The quotient is a terminating decimal.

5 858= 0.6625 Answer

)8 5 00048

2016

4040

0

0 625..

−

−

−

The fraction is already (or can be built up to) a decimal fraction (see page 457, Model 2)

Special Case:


►►B 31

16

31

163

116

= + The whole number 3 does not change.

Convert the fraction to a decimal. 116

)16 1 000096

4032

8080

0

0 0625..

−

−

−

The quotient is a terminating decimal. 31

16= 3.0625 Answer

►►C 512

)12 5 0000048

20128072807280

0 41666

728

.

.

−

−

−

−

−

The quotient is a non-terminating repeating decimal.

Rounded to the nearest ten-thousandth, 512

≈ 0.4167 Answer

Model 2 The Fraction is Already (or Can be Built Up to) a Decimal Fraction

Convert the following to decimals.

►►B

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.

►►A 910

THINK 910

is “nine tenths” or 0.9 Answer

8425

84 425 4

816100

××= THINK “eight and sixteen hundredths” 8.16 Answer

Special Case:


Technique

Multiply the decimal by 100%.

That is, move the decimal point two places to the right and attach the percent sign (%).

Converting a Decimal Number to a Percent

? ? ? Why can you do this?

Starting with a decimal number, for example 0.285, the Technique says that 0.285 × 100% = 28.5%.

The Identity Property of Multiplication states that multiplying any number by 1 does not change the value of the number. For this Technique, multiplying by 100% is multiplying by 1:

That is why the value of 0.285 does not change. Only its form changes.

Now consider the second part of the Technique. Why is it that, to multiply by 100%, you can simply move the decimal point two places to the right and add a percent sign? Think about the process this way: 0.285 × 100% = 28.5%

100100

1% means and, from your knowledge of fractions,

100 000

1001= .

The shortcut for multiplying by 100 is to move the decimal point two places to the right.THINK

Convert the following decimals to their equivalent percents.

0.8225

0.8225 × 100% = 82.25% OR 0.8225% = 82.25% Answer

1.723

1.723 × 100% = 172.3% OR 1.723% = 172.3% Answer

Models

►►A

►►B


0.04 0.04% = 4% Answer

0.009 0.009% = 0.9% Answer

4 4.00% = 400% Answer

►►C

►►D

►►E

Model 1

Technique

Drop the percent sign and divide the percent number by 100.

That is, drop the percent sign (%) and move the decimal point two places to the left.

Converting a Percent to a Decimal Number

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 defi nition of a percent as the ratio of the percent number to 100.

For example, = 28.5 ÷ 100 or 0.28528 528 5

100. %

.=

The shortcut for dividing by 100 is to move the decimal point two places to the left.THINK

85.4% 85.4% = 85.4 ÷ 100 = 0.854 OR 85.4% = 0.854 Answer

258% 258% = 258 ÷ 100 = 2.58 OR 258% = 2.58 Answer

2.3% 2.3% = 02.3% 0.023 Answer

0.75% 0.75% = 00.75% 0.0075 Answer

►►A

►►B

►►C

Convert the following percents to their equivalent decimals.

Zero place digit needed.

►►DTwo zero place digits needed.


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

►►B

6214

%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.

14= ÷ =1 4 0 25. so 62.25% = 62

14

% = 0.6225 Answer

1413

%

13

1 3 0 3 0 33= ÷ = ≈. .

1413

% .33%≈ 14 14.33% = 0.1433 Answer

Before looking at the remaining two techniques for converting between fractions and percents, think about the fi rst four conversion techniques, as summarized in the table below.

Fraction Decimal Percent

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 fi nal two conversion techniques.

1340

)40 13 000120

10080

200200

0

0 325..

−

−

−

0.325

0.325

and

× 100%32.5%

32.5%32 5100

.0.325

0.325

and

3251000

1340 reduce

Model 2


Technique

Step 1 — Convert the fraction or mixed number to a decimal.

Step 2 — Convert the decimal to a percent.

Converting a Fraction or a Mixed Number to a Percent

Special Case: The denominator is 100 (see below, Model 2)

Special Case: The denominator is a factor of 100 (see page 462, Model 3)

Special Case: The result of Step 1 is a repeating decimal (see page 462, Model 4)

Model 1

Convert the following to percents.

Step 1

Step 2 0.875% = 87.5% Answer

Step 1

Step 2 2.50% = 250% Answer

78

212

►►A

►►B

78

0 875= .

212

2 5= .

)8 7 0000 875

64

60

56

40

40

0

.

.

−

−

−

Model 2 Special Case: The Denominator of the Fraction is 100

Convert to a percent: 37

100

37100

= 37% Answer

If the denominator of the fraction is 100, the numerator IS the percent number.

)2 1 00 5

10

0

.

.

−


Model 3

Convert to a percent:

Step 1

Step 2 0.45% = 45% Answer

If the denominator of the fraction is a factor of 100, instead of dividing to determine the decimal, build the fraction to have 100 as its denominator. The numerator will be the percent number.

Special Case: The Denominator is a Factor of 100

9

20 920

0 45= .

)20 9 000 45

8 0

100

100

0

.

.

−

−

920

9 520 5

45100

= ××= = 45% by the definition of a percent.

Model 4 Special Case: The Result of Step 1 is a Repeating Decimal

Convert the fraction to a percent.

Round to the nearest hundredth percent, if necessary.

Step 1

Step 2 0.8333% = 83.33% 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.

5

6

56

0 8333≈ . )6 5 00000

48

20

18

20

18

20

18

20

18

2

0 83333..

−

−

−

−

−

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,

Another is to present the repeating decimal part as a fraction.

That is,

56

83 3= . %

56

8313

= % )6 5 00

48

20

18

2

0 83..

−

−

2

60 83

1

3= .


Technique

Step 1 — Convert the percent to its equivalent decimal.

Step 2 — Convert the decimal to its equivalent fraction or mixed number and reduce.

Converting a Percent to a Fraction or Mixed Number

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 3)

Model 1

0.06% Step 1 00.06% = 0.0006

Step 2

3.2% Step 1 03.2% = 0.032

Step 2

►►A

►►B

0 00066

10 0006 2

10 000 2.

, ,= = ÷

÷= 3

5000 Answer

0 03232

1 00032 4

1 000 48 2

250 2.

, ,= = ÷

÷= ÷

÷= 4

125 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 54%

215%

When the percent number is a whole number, there is no advantage to using its decimal equivalent. Simply write the percent number over 100 (defi nition of percent) and reduce.

54 0 5454 2100 2

% .= = ÷÷= 27

50 Answer

5454 2100 2

% = ÷÷= 27

50 Answer

►►B 215215100

215

100

3

20% = = = 23

20 Answer

Convert the following to fractions or mixed numbers. Reduce the fractions to lowest terms.


Model 3 Special case: The Percent Number Contains a Fraction

Convert the following to fractions. Reduce to lowest terms.

►►A

Note: This procedure assures that the resulting fractions will be the exact equivalent of the percent.

When the percent number contains a fraction, drop the percent sign and multiply the percent number by 1/100 (same as dividing the percent number by 100). Reduce the fraction.

►►B

2316

%

2316

2316

10023

16

1100

1396

1100

% = = × = × = 139600

Answer (reduced fully)

►►C

212

%

212

212

1100

52

1

100

1

20% = × = × = 140

Answer

Note: Since the ½ in the percent number can be converted to a terminating decimal, 0.5, you can choose to work through the decimal and convert as follows:

212

02 5 0 02525 25

1000 25140

% . % .= = = ÷÷

=

3313

%

3313

3313

1100

1003

1

100

1

1% = × = × = 13

Answer


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 1: Decimal to Fraction

Conversion:

Validation:

Example 2: Fraction to Decimal

A. Conversion:

Validation: (Convert 0.625 to a fraction)

B. Conversion:

Validation: Since 0.417 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.

Example 3: Decimal to Percent

Conversion: 1.723 = 172.3% Answer

Validation: (Convert 172.3% to a decimal.)

172.3% = 1.723

0.22 = 1150

Answer

)50 11 0010 0

100100

0

.−

−

0.22

(Convert to a decimal)1150

58= 0 625. Answer

0.625 =625 25

1000 2525 540 5

÷÷

= ÷÷= 5

8

512

≈ 0 417. Answer (rounded)

4171000

417 12 5 10005004 5000

=

× = ×≈

512

?

?

continues on the next page


Example 4: Percent to Decimal

A. Conversion: 2.3% = 0.023 Answer

Validation: (Convert 0.023 to a percent)

0.023% = 2.3%

B. Conversion:

Validation: (Convert 0.6225 to a percent)

Example 5: Fraction to Percent

A. Conversion:

Validation: (Convert 45% to a fraction)

B. Conversion:

Validation: Change the rounded 83.33% to its decimal equivalent. Then validate the equality of the decimal fraction and the original fraction.

Example 6: Percent to Fraction

Conversion:

Validation:

6214

% = 0 6225. Answer

0 6225 62 25 6225100

. . % %% = = = 6214

%

920= 45% Answer

45 0 4545 5

100 5% .= = ÷

÷= 9

20

56

≈ 83 33. % (rounded)

83 33 0 83338 333

10 0008 333 6 5 10 000

49 998 50 000

. % .,,

, ,, ,

=

=

× = ×≈

56

?

?

0.6% = 3500

Answer

(Convert to a percent.)3

500

)500 3 0003000

0

0 006..

−0 006. % = 0.6%


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 (< 1)

Example:

< 1.0

Example: 0.4

< 100%

Example: 40%

improper fraction or mixed number (> 1)

Example:

> 1.0

Example: 1.75

> 100%

Example: 175%

Example: Convert 0.22 to a fraction.

Prediction: Since 0.22 < 1, the fraction will be proper (< 1).

Actual answer:

Example: Convert to a percent.

Prediction: Since < 1, the percent will be < 100%.

Actual answer: 87.5%

Example: Convert 1.6 to a percent.

Prediction: Since 1.6 > 1.0, the percent will be > 100%.

Actual answer: 160%

You can, in fact, refi ne 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

< 0.5 < 50%

< 0.1 < 10%

> 0.5 > 50%

> 0.75 > 75%

> 2 > 2.0 > 200%

25

134

THINK

1150

THINK

7

8

THINK

< 12

< 110

> 12

> 34

7

8

How Estimation/Prediction Can Help



Prediction: Since 0.22 < 0.5, the fraction will be < ½ .

Actual answer:

Example: Convert to a percent.

Prediction:

Actual answer: 87.5%


Prediction: Since 2.8 > 2.0, the percent will be > 200% and since 2.8 > 2.5, the percent will be > 250%.

Actual answer: 280%

Example: Convert 240% to a fraction.

Prediction: Since 240% > 200%, the fraction will be a mixed number > 2 and

Since 40% < 50%, the fraction part of the mixed number will be

Actual answer:


Prediction: Since 0.07 < 0.1, the fraction will be

Actual answer:


Prediction: Since 0.07 < 0.1, the percent will be < 10%.

Actual answer: 7%

THINK

1150

<⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

1

2

25

50 or

7

8

THINK Since 7

8 , the percent will be >⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟ >3

4

6

875%

THINK

THINK

225

THINK < 1

10.

THINK

7100

<⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟

1

10

10

100 or

< 1

2.


Technique

Step 1 — Convert all numbers to the same equivalent form.

Step 2 — Order them as you would for your chosen form.

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 3). 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 effi cient.

Model

List the following in order of their values, from lowest to highest: , 0.115, 11%

Step 1: Write as decimals. Step 2: Order the decimals using trailing zeros. Rank

0.111 2

0.115 is in decimal form 0.115 3

11% = 0.11 0.110 1

List the following in order of their values, from lowest to highest:

Step 1: Write as decimals. Step 2: Order the decimals using trailing zeros. Rank

0.75 = 0.75 0.7500 3

0.0075 1

7.5% = 07.5% 0.0750 2

►►A

►►B

19

0 1 0 111= ≈. .

Answer : 11%19

, 0.115 ,

1

9

)9 1 000

9

10

9

10

9

1

0 111..

−

−

−

0 753

47 5. % . %, ,

Answer : 34

% , 7.5% , 0.75

34

% .75%= =00 0 0075.

TTECHNIQUEECHNIQUE

Ordering a Mixed Set of Decimals, Fractions, and Percents


AADDRESSING DDRESSING CCOMMON OMMON EERRORSRRORS

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 decimal.

Convert 2.35% to a fraction.

Answer:

Converting the fraction in the percent number to a decimal or the decimal in the percent number to a fraction only changes the form of the percent number.

Drop the percent sign (%) only when you divide the percent number by 100.

Convert to a decimal.


Making an error in the shift of the decimal point when converting between decimals and percents

Convert 1.5 to a percent.

1.5 = 0.015%

Convert 2.27% to a decimal.

2.27% = 227

When converting from a decimal to a percent, the resulting percent number will always be 100 times as large as the decimal number.

When converting from a percent to a decimal, the resulting decimal number will always be 100 times smaller than the percent number.

Think about the decimal point shift in a conversion you know.

25 converts to 25% and

25% converts to 0.25

0.25 25%

Decimal Percentpoint shifts right

Decimal Percentpoint shifts left

Convert 1.5 to a percent.

1.5 > 1 so the percent will be greater than 100%

1.5 × 100% = 150%

Convert 2.27% to a decimal.

2.27% < 100%, so the decimal will be less than 1.

02.27% = 0.0227

135

1 6

01 6

% . %

. %

=

= 0.016

135

% 135

%

)5 3 030

0

0 6..

−

2 35 235

100

7

20. % =

2720

2 35 0 0235235 5

10 000 5

. % .

,

=

= ÷÷

= 472,000

THINK

THINK

5) 00 6

)5 3)30

52

. 0=

% 2=


Issue Incorrect Process Resolution Correct Process

Not presenting the required fraction form when converting from a percent to a fraction


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.


Misinterpreting the denominator for the decimal fraction when converting from a decimal to a fraction

Convert 0.125 to its fraction equivalent.

Review Section 2.1 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 0.125 to its fraction equivalent.

0 80 8 4100 4

. %.= ÷÷

Answer = 0 225.

0 8 00 8 0 008. % . % .= =

0 0088

1000

1

125. =

= 1125

0 125125 1251000 125

. = ÷÷

= 18

0 125125 125

10 000 125

5

400

180

1

80

.,

= ÷÷

= =

%80100

120,

25 1212500


PPREPARATION REPARATION IINVENTORYNVENTORY

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

473

ACTIVITY

Converting between Percents,

Decimals, and Fractions

PPERFORMANCE ERFORMANCE CCRITERIARITERIA

• 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

CCRITICAL RITICAL TTHINKING HINKING QQUESTIONSUESTIONS

1. When writing a decimal fraction for a given decimal number, how do you determine its denominator?

2. What are two ways to convert a fraction to decimal? For each procedure, when and why would you choose to use it?

3. What are the two required characteristics of the fi nal answer for a decimal to fraction conversion?

Section 5.1


4. Why does

5. Why is a percent called a special type of ratio?

6. What are four ways to convert fractions to percents? For each procedure, when and why would you choose to use it?

•

•

•

•

100100

1001% = = ?


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?

•

•

•

8. How can you be sure that you have moved the decimal point in the proper direction when converting between decimals and percents?

9. What does a decimal or a fraction within a percent mean?


10. How can you go about ordering a mixed set of fractions, decimals, and percents?

• 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.

TTIPS FOR IPS FOR SSUCCESSUCCESS

Fraction Decimal Percent

Begin with a Fraction0.75 75%

Begin with a Decimal0.5 50%

0.25Begin with a Percent

25%

34

14

25100

←

12

50100

←

• Use estimation/prediction to assure that your answer “makes sense.”

• Know some of the most common conversions:

1

1010

1

425

1

250 75 33= = = = =% % % %, , ,

3

4,

1

3

11

366

2

3% %,

2

3=


DDEMONSTRATE EMONSTRATE YYOUR OUR UUNDERSTANDINGNDERSTANDING

Convert to a Fraction or

Mixed NumberProcess Answer Validation (optional)

a) 0.03

b) 0.156

c) 8.42

1. Convert each of the following to a simple fraction or mixed number. Reduce to lowest terms.

Convert to a Decimal Process Answer Validation (optional)

a)

b)

2. Convert each of the following to a decimal. Round to the nearest thousandth for non-terminating decimals.

1740

1500


Convert to a Decimal Process Answer Validation (optional)

c)

d)

e)

f)

27

11320

445

716


Convert to a Percent Process Answer Validation

(optional)

a) 1.25

b) 0.3

c) 0.0785

d) 0.0005

e) 3

f) 10.25

3. Convert each of the following to a percent.

Convert to a Decimal Process Answer Validation

(optional)

a) 34%

b) 2.57%

c) 0.74%

d) 382%

e) 3%

f)

g)

4. Convert each of the following to a decimal. Round to the nearest ten-thousandth, if necessary.

2412

%

623

%


Convert to a Percent Process Answer Validation (optional)

a)

b)

c)

d)

5. Convert each of the following to a percent. Round to the nearest hundredth percent, if necessary.

316

750

338

112


Convert to a Percent Process Answer Validation (optional)

e)

f)

134

1512

100



a) 125%

b) 38%

6. Convert each of the following to a simple fraction or mixed number. Reduce to lowest terms.




c)

d)

e) 0.74%

f) 0.8%

g) 62.5%

6123

%

334

%


7. Order the following from lowest to highest value:

8. Order the following from highest to lowest value:

3

838 0 34, %, . , 37%

5 31

200 555. %, , . , 5

1

2%,

1

2

TEAM EXERCISESTEAM EXERCISES

1. In the grids below, fi ll in the correct number of rectangles to represent the following: a) 4% Use a pencil. c) 140% Use a highlighter. b) 30% Use a pen. d) 0.6% Use a different color highlighter.


2. Fill in 17% of this grid.

3. What percent of this fi gure is unshaded?

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?


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 SolutionWhat is Wrong Here? Identify the Errors Correct Process

1) Write the equivalent fraction for 0.72%.

The fraction form should not contain a decimal point.

Convert the percent to a decimal, then to a fraction.

Reduce the fraction.

2) Change 5.5% to a fraction.

3) Write 1.12% as a fraction.

4) Write 0.005 as a percent.

IDENTIFY AND CORRECT THE ERRORSIDENTIFY AND CORRECT THE ERRORS

00 72 0072. % .=

= ÷÷

=72 410 000 4

182 500, ,

18 22 500 2

91 250

÷÷

=, ,

Answer:9

1 250,


235

Worked SolutionWhat is Wrong Here? Identify the Errors Correct Process

5) Convert 17.3 to a percent.

6) Convert to a percent.


Convert each of the following to a decimal. Round to the nearest ten-thousandth, if necessary.

1. 5.

2. 126% 6. 48%

3. 7.

4. 8.

Convert each of the following to a percent. Round to the nearest hundredth percent, if necessary.

9. 0.325 13. 0.006

10. 14.

11. 15.

12. 0.23 16.

Convert each of the following to a simple fraction or mixed number. Reduce to the lowest term.

17. 0.275 21. 4.8%

18. 2.65 22. 264%

19. 17.5% 23. 96%

20. 24.

Order the following from smallest to largest.

25.

26.

3

5

4

9

23

4%

45

8

5

11

121

6%

5

16

11

25

1

3

51

4

13

5

51

4% 66

2

3%

5

80 632 62 9, . , . %,

11

16

1 4 13

8. , , ,

29

20 142.5%

ADDITIONAL EXERCISESADDITIONAL EXERCISES

p -a decimals, and fractions p · pdf fileconverting between fractions, decimals, ......

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