Reading Assignment—Notes and Questions

123Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers

Reading Assignment—Notes and Questions

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I have questions to ask in class about specifi c parts of the assignment that were unclear— PageQuestion Number

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Notes

124 Foundations of Mathematics

Problem-solving Assignment—Notes and Questions

Name___________________________________________ Date_______________

Problem-solving Assignment: Foundations workbook: Section#_________ Pages_______________

Textbook: Section#_________ Pages_______________

I have questions to ask in class about specifi c parts of the assignment that were unclear— PageQuestion Number

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125

PRE-ACTIVITY

PREPARATION

Financial transactions in dollars and cents are perhaps the most common examples of how you use decimal numbers in your daily life. Your understanding of decimal place values and the proper placement of the decimal point are very important when dealing with money, as you know. Imagine your frustration if you expect a $652.00 paycheck, only to receive one for $65.20! When you write your own personal checks, as well, you must write the amounts properly in both digits and words.

There are other than monetary applications of decimals, of course. Your cumulative grade point average (GPA) and sports statistics such as batting averages or race times are common examples. Accuracy in presentation is also of great importance in the fi elds of science, medicine, engineering, manufacturing, and architectural design for which measurements are most often given in the form of decimal numbers.

You may come across rounded decimal numbers as well—

• advertised prices—$5 for 3 boxes of crackers or, rounded to the nearest cent, $1.67 to purchase a single box

• estimated weight measurements—your scanned purchase of 3.2 pounds of apples from the produce section or 1.94 pounds of cheese from the deli

• census statistics presenting larger numbers, such as Michigan’s estimated population of 10.1 million residents or the 17.5 million college students in the United States

Before using the four basic operations of addition, subtraction, multiplication, and division to compute with decimal numbers, you should have a working knowledge of how reading, writing, comparing, and rounding decimal numbers are made easier by the design of the decimal number system.

• Properly read and write a decimal number.

• Put any set of decimal numbers in order.

• Master the process of rounding a decimal number to a given decimal place value.

Reading, Writing, Comparing, and Rounding Decimal Numbers

Section 2.1

LLEARNINGEARNING OOBJECTIVESBJECTIVES

126 Chapter 2 — Decimal Numbers

BBUILDING UILDING MMATHEMATICAL ATHEMATICAL LLANGUAGEANGUAGE

From your study of whole numbers, you know that when you write a number in its standard formin the decimal (base ten) system, every position in the number has a corresponding and specific place value.

Note the partial decimal system place value chart on the next page. The chart for whole numbers is extended to also include the place values to the right of the ones place—places used to represent numbers less than one (1), places representing fractional parts of one whole unit.

What do the phrases “a number less than one (1)” and “fractional parts” mean? If you think in terms of money, you know, for instance, that $2.38 is more than $2 and less than $3. Similarly, when the gas pump displays your purchase of 15.29 gallons of gas, you know that you have put in more than 15 gallons but less than 16 gallons. That $ .38 represents less than $1 or part of one dollar and the .29 gallons represents a fractional part of one gallon of gas.

When a decimal number is written in standard form (standard decimal notation), a decimal point separates its whole number part from its fractional part.

The places to the right of the decimal point, beginning with the tenths, are commonly referred to as the decimal places. Because they are fractional parts, their place names all end with “ths.”

NEW TERMS TO LEARN

compare

decimals

decimal number

decimal places

decimal place digit

decimal point

hundredths

hundred-thousandths

order

standard decimal notation

tenths

ten-thousandths

thousandths

trailing zeros

PREVIOUSLY USED

base ten system

decimal system

expanded form

greater than symbol >

less than symbol <

midpoint

number line

place digit

place value

round down

round up

standard form

TTERMINOLOGYERMINOLOGY


The number 15.29 (“fifteen and twenty-nine hundredths”) is positioned properly in the chart below.

It is important to note that, as you move from left to right in the chart, each place value is equal to the place value to its left divided by 10. The place values grow smaller as you move to the right. The pattern is:

You can think of this pattern in its reverse as well. As you move from right to left, the place values grow larger, as each place value represents 10 times the place value to its immediate right:

When there is no whole number part, a decimal number may be written with or without a zero (0) as the placeholder digit for the ones place. For example,

.275 can also be written as 0.275Both are read, “two hundred seventy-five thousandths.”Both denote a number less than one (1).

Writing a zero in the ones place helps to assure that you will not overlook the decimal point when working with decimal numbers.

For a whole number, the decimal point is understood to be to the immediate right of the ones place digit.A whole number is usually written without the decimal point, unless it is necessary to use it for an operation that involves other decimal numbers. For example, 29 can be written as 29. or 29.0 if necessary.

Place name

Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths Ten-Thousandths

Place value

1000 100 10 1 . .1 .01 .001 .0001

Example number 1 5 . 2 9

1000 ÷ 10 = 100 one hundred 100 ÷ 10 = 10 ten 10 ÷ 10 = 1 one 1 ÷ 10 = .1 one tenth .1 ÷ 10 = .01 one hundredth .01 ÷ 10 = .001 one thousandth, and so on as you move left to right in place value.

10 × .001 = .0110 × .01 = .110 × .1 = 110 × 1 = 1010 × 10 = 10010 × 100 = 1000, and so on as you move left in place value


Dividing 1 into 10 equal parts

Dividing 1 into 100 equal parts and so on, as

the fractional parts of one whole units become smaller when each part is sub-divided into 10 equal parts.

You might find it helpful to visualize the parts of one whole unit represented by the place values to the right of the decimal point (the decimal places).

The shaded areas in the figures below represent the place values 1, .1, and .01:

How might you visually represent .8 (eight tenths) in the figure below?

How might you visually represent .29 (twenty-nine hundredths) in the figure below?

.1 or 110

"one tenth"

.01 or 1

100"one hundredth"

1


This book will refer to the zeros appended to the right of the digits after the decimal point as trailing zeros. For example, 8.36 = 8.360 = 8.3600 = 8.36000, and so on.

Trailing zeros do not change the value of the number. Why? Recall that a zero used as a placeholder signifies a value of zero for that place. For example, 8.360 in its expanded form is 8 ones + 3 tenths + 6 hundredths + 0 thousandths or 8 ones + 3 tenths + 6 hundredths + 0 or 8 .36

A number line can help you visualize the comparison of decimal numbers. As with whole numbers, the farther you move to the right on a number line, the larger the number will be. On the number line below, 2.1 is larger than 2.0, 2.9 is larger than 2.1, and 3.0 is larger than 2.9.

To indicate the decimal numbers between 2.1 and 2.2, zoom in on that section and divide it into appropriate equal intervals. For example, 2.11, 2.15, and 2.18 are properly indicated on the number line below.

The word “and” is used to signify the placement of the decimal point when reading or writing a decimal number in its word form. For example, 48.63 in word form is “forty-eight and sixty-three hundredths.”

The term “decimals” is often used interchangeably with the term “decimal numbers” as in the sentence, “In some applications, you might think it easier to compute with decimals than with fractions.”

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20

You may be accustomed to hearing or reading aloud the common translation of a decimal number, say 91.0815, as “ninety-one point zero eight one five.” However, keeping in mind the decimal system place value chart, you can use the following two techniques to translate between the standard form and word form of decimal numbers in correct math terminology. The first provides the proper way to express a decimal number in words, and both techniques underscore what the fractional part of a decimal number actually means.

To verify your translated answer, you can use the opposite technique.

Reading and Writing Decimal Numbers


TTECHNIQUEECHNIQUE

Translating a Decimal Number from Standard Form to Word Form

Technique

Step 1: If there is a whole number part (left of the decimal point), say or write out its word name and translate the decimal point as “and.” If there is no whole number part, skip to Step 2.

Step 2: Say or write the number formed by the digits to the right of the decimal point and attach the place value name of the fi nal digit (farthest to the right).

MMODELSODELS

Translate each of the following numbers to its word form.

►►B►►A 502.467

Step 1: fi ve hundred two and

Step 2:

.te

nth

s

hundre

dth

s

tho

usa

nd

ths

4 6 7

four hundred sixty-seven thousandths

Answer: fi ve hundred two and four hundred sixty-seven thousandths

91.0815

Step 1: ninety-one and

Step 2:

.te

nth

s

hundre

dth

s

thousa

ndth

s

ten

-th

ou

san

dth

s

0 8 1 5

eight hundred fi fteen ten-thousandths

Answer: ninety-one and eight hundred fi fteen ten-thousandths

Special Case:

Zero (0) as the whole number (see page 131, Model C)


►►C 0.10275

Step 1:

Step 2:

.te

nth

s

hundre

dth

s

thousa

ndth

s

ten-t

housa

ndth

s

hu

nd

red

-th

ou

san

dth

s

Answer: ten thousand two hundred seventy-fi ve hundred-thousandths

1 0 2 7 5

TTECHNIQUEECHNIQUE

Translating a Decimal Number from Word Form to Standard Form

Technique

Step 1: Write the whole number (words before “and”) in its standard form and substitute a decimal point for the word “and.”

Step 2: Translate the word name of the fractional part to digits in standard form, aligning its fi nal digit with the named decimal place value.

Step 3: Use a zero (0) placeholder if a decimal place is missing.

When the whole number is zero, it is not necessary to say or write “zero and” for the whole number name and decimal point. Skip to Step 2.

Special Case:

No whole number part in the word form (see page 133, Model D)

Special Case: Zero (0) as the Whole Number


Translate each of the following numbers to its standard form.

►►A “four hundred six and twenty-one hundredths”

Step 1: 406.

Step 2: twenty-one hundredths

Step 3: all decimal places accounted for— no zero decimal place holders needed.

Answer: 406.21

MMODELSODELS

tenth

s

hundre

dth

s

2 1

►►B

►►C

“ninety-four and two hundred seven hundred-thousandths”

Step 1: 94.

Step 2: two hundred seven hundred-thousandths

Step 3:

Answer: 94.00207

tenth

s

hundre

dth

s

thousa

ndth

s

ten-t

housa

ndth

s

hundre

d-t

housa

ndth

s

0 0 2 0 7

zero placeholders for the missing decimal places

“three and fi fty hundredths”

Step 1: 3.

Step 2: fi fty hundredths

Step 3: all decimal places accounted for

Answer: 3.50

tenth

s

hundre

dth

s

5 0


►►D “eighty-three thousandths”

Step 1: 0.

Step 2: eighty-three thousandths

Step 3: zero placeholders for the missing tenths place

Answer: 0.083

If there is no whole number part in the word form, use zero (0) as the whole number, followed by a decimal point, to assure the decimal point is properly placed.

tenth

s

hundre

dth

s

thousa

ndth

s

0 8 3

You already know how to compare values of whole numbers; that is, determine which number is smaller and which is larger. The process is almost automatic. For example, to compare 461 and 428 you look to the tens place digits. Knowing that 6 tens are greater than 2 tens, you can readily say 461 > 428.

You can also compare decimal numbers place value by place value.

For example, which is smaller, 0 .825 or 0 .823?

You see that the digit 8 occupies the tenths place in each number and that there is a 2 in both hundredths places.

However, in the thousandths place, the digits are different. The thousandths place digit 3 is less than the thousandths place digit 5.

Now you can say with certainty that 0.823 < 0.825. That is, eight hundred twenty-three thousandths is less than eight hundred twenty-fi ve thousandths.

How can you order, arrange from smallest to largest or largest to smallest, any list of decimal numbers? The following methodology offers a simple and effective way to do so that takes advantage of your ability to compare whole numbers.

samesame

different

Special Case: No Whole Number Part in the Word Form

Comparing the Values of Decimal Numbers


MMETHODOLOGYETHODOLOGY

Comparing (Ordering) Decimal Numbers

Example 1: 3.25, 3.6, 4.3, 3, 3.384 Example 2: 6.219, 5.201, 6.3, 6.21, 6.02►►

Steps in the Methodology Example 1 Example 2

Step 1

List the numbers.

Write the numbers in a column, aligning place values and decimal points.

3.253.64.33.3.384

Step 2

Sort by whole numbers.

Arrange the numbers in the desired order (smallest to largest or largest to smallest) according to their whole numbers (ignoring the decimal places).

3.25

3.6

3.

3.384

4.3

Step 3

Append trailing zeros.

For the set of numbers with the same whole number part, use trailing zeros so that each number ends with the same place value.

3.25 3.250

3.6 3.600

3. 3.000

3.384 3.384

4.3 4.3

Step 4

Order by fractional parts.

Order the set according to the fractional parts. 3.25 3.250

3.6 3.600

3. 3.000

3.384 3.384

4.3 4.3

Step 5Present the fi nal answer.

Write the original numbers in the correct order. 3, 3.25, 3.384, 3.6, 4.3

? ? ? ? ?Why can and why do you do this?

Try It!►►

smallest to largestRank

5

Rank

5

Rank2

4

1

3

5

THINK

0 < 250 < 384 < 600

Order the following list of numbers from smallest to largest.

Special Case:

Two or more whole number sets to order in the list (see page 135, Model)


? ? ? ? ?Why can and why do you do Step 3?

Trailing zeros do not change the value of the decimal numbers.

When you make the decimal numbers all end with the same fractional place, you can easily compare fractional parts according to the entire series of digits occupying those places.

In Example 1 you can now simply compare 250 thousandths to 600 thousandths to 000 thousandths to 384 thousandths. Arranging 250, 600, 000, and 384 is an easy task:

0 thousandths < 250 thousandths < 384 thousandths < 600 thousandths

MMODELODEL

Arrange the following list of numbers in order from largest to smallest.

1.7087, 0.078, 0.87, 1.781, 0.0877, 0.8

Step 2 largest to smallest

Step 1 1.7087 1.7087 0.078 1.781

set of numbers with 1 as the whole number

0.87 0.078 1.781 0.87 0.0877 0.0877

set of numbers with 0 as the whole number

0.8 0.8

Steps 3 & 4 Rank

1.7087 1.7087 2

1.781 1.7810 1

0.078 0.0780 6

0.87 0.8700 3

0.0877 0.0877 5

0.8 0.8000 4

Step 5 Answer: 1.781, 1.78087, 0.87, 0.8, 0.0877, 0.078

}

}When there are two or more whole number sets in the list, order each set separately, using trailing zeros as appropriate. Then combine the rankings for the fi nal order.

THINK 7810 > 7087

THINK 8700 > 8000 > 877 > 780

Special Case: Two or More Whole Number Sets to Order in the List


The methodology for rounding decimal numbers uses the concept of a midpoint (middle) number to make the decision whether to round up or round down, as did the methodology for rounding whole numbers (refer to Section 1.2).

Note that the methodology will refer to the digit in a specifi ed decimal place as the decimal place digit.

MMETHODOLOGYETHODOLOGY

Rounding a Decimal Number

Example 1: Round 43.9738 to the nearest hundredth. Example 2: Round 24.61809 to the nearest thousandths place.►►


Step 1

Determine fi nal number of decimal places.

Determine the number of decimal places in the fi nal answer.

hundredth

The fi nal answer will have two

decimal places.

Step 2

Identify the place digit.

Identify the digit in the specifi ed place value (the place digit) by marking it with an arrow.

4 3 . 9 7 3 8

Step 3

Identify the digit to the right of the place digit.

Identify the digit occupying the decimal place immediately to the right of the place digit by circling it. 4 3 . 9 7 3 8

Step 4

Compare to the number 5.

Determine whether the circled digit is less than, equal to, or greater than 5. 3 < 5

Step 5

Round up or down.

If the circled digit is less than 5, do not change the place digit.

If the circled digit is 5 or greater, round up by adding one to the place digit.

The hundredths place digit does not change

4 3 . 9 7 x x

Try It!►►

? ? ? Why do you do this?

Special Case:

Rounding to the nearest whole number (see page 138, Model 1)

Rounding Decimal Numbers



Step 6

Present the fi nal answer.

To present your fi nal answer, drop all decimal place digits to the right of the specifi ed place value.

43.97

The last decimal place value for a rounded answer will always be named, so the fi nal answer must have only as many decimal places as specifi ed to refl ect the corresponding fractional part.

In Example 1, the named hundredths place requires two and only two places to the right of the decimal point.

As the result of rounding, the digits to the right of the specifi ed place value digit become zeros (just as they did with whole numbers).

They are trailing zeros, however, because of their positions in the decimal number. Therefore, they can be dropped without changing the value of the rounded decimal number.

? ? ? Why can you do this?

? ? ? Why do you do Step 1?

? ? ?Why can you do Step 6?

Special Case:

Presenting a zero in the specifi ed place value(see page 138, Model 2)


Model 1

MMODELSODELS

Model 2

Round 246.547 to the nearest whole number.

Step 1 no decimal places (Round to the ones place.)

Step 2 246.547

Step 3 246.547

Step 4 5 = 5

Step 5 The 6 changes to a 7.

Step 6 Answer: 247. or 247

Rounding to the nearest whole number means rounding to the ones place.

Round 12.3997 to the nearest hundredths place.

Step 1 2 decimal places (Round to the hundredths place.)

Step 2 12.3997

Step 3 12.3997

Step 4 9 > 5

Step 5 The 9 changes to 0 and carry the 1 to the tenths place, making it a 4. 12.40xx

Step 6 Answer: 12.40 After rounding up or down, if the specifi ed decimal place digit is zero (0), it is necessary to present it in the answer to indicate that the original number has been rounded to that place.

Pictured on a number line:

246 247246.5

246.547

midpoint

Pictured on a number line:

12.39 12.395

12.3997

midpoint

12.40

Special Case: Rounding to the Nearest Whole Number

Special Case: Presenting a Zero in the Specifi ed Place Value


AADDRESSING DDRESSING CCOMMON OMMON EERRORSRRORS

Issue Incorrect Process Resolution Correct Process

Reading decimal numbers incorrectly when there are zeros as decimal place holders in the standard form

36.052 is read as “thirty-six and

fi fty-two hundredths”

Use the place value chart and align the digits with the chart.

36.052 is read as “thirty-six and

fi fty-two thousandths”

Comparing without regard to decimal place values

Compare:4.0387 and 4.38

4.0387

is larger than

4.38

It is not the number of digits after the decimal point that determines order, but the place value of those digits.

Use trailing zeros (that is, append zeros so the numbers have the same place values) so you can make a true comparison of their fractional parts.

Compare:4.0387 and 4.38

4.0387 4.03874.38 4.3800

Incorrectly identifying decimal places when rounding

Round 87.6349 to the nearest hundredth.

Thinking, “ones, tenths, hundredths

… the 4 is in the hundredths’ place.”

87.6349

Answer: 87.635

The whole number is to the left of the decimal point, starting with the ones. The fractional part of a whole is to the right, starting with the tenths.

In 87.6349, the 3 is in the hundredths place.

87.6349

Answer: 87.63

Incorrectly presenting the fi nal rounded decimal number

32.9179 rounded to the tenths place

is 32.9000

Rounding decimals requires dropping the digits to the right of the specifi ed place.

For example, rounding to tenths means there will be only one number to the right of the decimal point.

32.9179 rounded to the tenths place

is 32.9

tenth

s

hundre

dth

s

thousa

ndth

s

3 6 . 0 5 2

THINK 387 > 38

3800 ten-thousandths >387 ten-thousandths

THINK 3800 > 387

Therefore,

4.38 > 4.0387

5hiwo hhun

2 is rex d

52 y-s

und

3

4

a

4 338

.0387

h

4.0

er t

87

we 8

49

7

7.6

87

1es 3 9

179 ros

0

917tent

90


PPREPARATION REPARATION IINVENTORYNVENTORY

Before proceeding, you should have an understanding of each of the following:

the terminology and notation associated with reading, writing, comparing, and rounding decimal numbers

the identifi cation of place values

the value of a digit with respect to its particular position in a decimal number

the placement of the decimal point in a whole number

the use of trailing zeros as an effective method for comparing (ordering) decimal numbers

the correct presentation of a rounded decimal number

Issue Incorrect Process Resolution Correct Process

Not presenting zero as a decimal place holder to indicate designated accuracy in a rounded answer

Round 73.0348 to the nearest tenth.

73.0348

Answer: 73

When rounding to a designated place value, the fi nal answer must present the specifi ed number of decimal places to indicate that level of accuracy.

Round 73.0348 to the nearest tenth.

Rounding to tenths means there must be one decimal place in the fi nal answer.

73.0348 rounded to the nearest tenth

is 73.0

3

swer:

.03483.0

7

141

ACTIVITY

Section 2.1

PPERFORMANCE ERFORMANCE CCRITERIARITERIA

• Translating between standard decimal notation and words – correct identifi cation and interpretation of each given place value – correct use of “and” or the decimal point – correct use of place value names

• Arranging a set of decimal numbers in order from smallest to largest or largest to smallest – appropriate use of trailing zeros – correct comparisons

• Rounding decimal numbers to specifi ed place values – correct identifi cation of the specifi ed place value – consistent documentation and presentation with appropriate notation – accuracy in the rounding process

CCRITICAL RITICAL TTHINKING HINKING QQUESTIONSUESTIONS

1. What are three real-world examples for which decimal numbers are used?

•

•

•

2. How is the whole number part separated from the decimal fraction part in reading and writing a decimal number?

Reading, Writing, Comparing, and Rounding Decimal Numbers


3. How can any whole number be expressed as a decimal number?

4. What are the names of the three decimal place values to the right of the thousandths place?

5. What does it mean to use zero (0) as a decimal placeholder?

6. Why can you add trailing zeros to a decimal number without changing the value of the number?

7. What is the relationship between ones and tenths? between tenths and hundredths?


8. How can you make sure that you order a set of decimal numbers correctly?

9. What is the most signifi cant difference between rounding whole numbers and rounding decimal numbers?

10. When would you present a zero (0) as the fi nal decimal place digit in a rounded answer?

11. In the U.S. monetary system, why are dollar amounts rounded to two decimal places?


TTIPS FOR IPS FOR SSUCCESSUCCESS

• Know the place value chart.

• To assure your translation is correct, cover up the original representation of the decimal number. Then convert back to see if you can get the same number, in digits or words.

• Use trailing zeros when comparing decimal numbers.

• Use consistent notation for the rounding process.

• Drawing a number line may help to visualize the comparison to the midpoint number in the rounding process.

DDEMONSTRATE EMONSTRATE YYOUR OUR UUNDERSTANDINGNDERSTANDING

1. Identify the place indicated.

a) 5.046 The 6 is in the __________________________________________ place.

b) 359.20 The 2 is in the __________________________________________ place.

c) 0.6974 The 0 is in the __________________________________________ place.

2. Write the following numbers in standard decimal notation.

a) Three thousand four hundred and six tenths _____________________________________

b) Five hundred thirty-two thousandths __________________________________________

c) Six thousand and forty-nine ten thousandths ____________________________________

d) Eight and three hundred seven hundred-thousandths ______________________________

3. Write in words.

a) 203.52 _________________________________________________________________

_________________________________________________________________

b) 48.0057 _________________________________________________________________

_________________________________________________________________

c) 0.906 _________________________________________________________________

_________________________________________________________________

d) 0.75201 _________________________________________________________________

_________________________________________________________________


4. Order the following numbers from smallest to largest: 2.046, 2.4, 1.06, 2, 2.46

Solution:

Answer:

5. Order the following numbers from smallest to largest: 24.07, 24.007, 24.005, 24.058, 24.0059

Solution:

Answer:

6. Order the following numbers from largest to smallest: 0.05, 1.03, 1.9, 0.1, 0.201

Solution:

Answer:


7. Round 713.54973 to the indicated place.

713.54973 Rounding Process Answer

a) tenth

b) hundredth

c) thousandth

d) ten-thousandth

e) hundred

f) nearest whole number

1. In the grids below, fi ll in the correct number of rectangles to represent the following decimal numbers. (Hint: you may fi nd it helpful to use trailing zeros.)

a) 0.17 Use a pencil. b) 0.04 Use a pen. c) 0.5 Use a highlighter. d) 1.4 Use a different color highlighter.

e) How could you modify one of the grids to shade in a representation of the decimal number 0.006?

TEAM EXERCISESTEAM EXERCISES


•

•

•

•

•

•

•

•

•

•

2. List fi fteen decimal numbers between 0.25 and 0.26 •

•

•

•

•

IDENTIFY AND CORRECT THE ERRORSIDENTIFY AND CORRECT THE ERRORS

Identify and correct the errors, if any, in the following worked solutions. If the answer is correct, write “Correct” in the second column. If the worked solution is incorrect, solve the problem correctly in the third column. The fi rst one has been done for you.

Worked SolutionWhat is Wrong Here? Identify the Errors Correct Process

1) Round 62.3585 to the nearest hundredth. Round to the thousandths

place, not the specified hundredths place.

62.3585

2) Write in words: 5.036.

3) Round 5.6719 to the nearest hundredth.

4) Round 88.9673 to the nearest tenth.

5) Round 4.1357 to the nearest whole number.

Answer: 62.36


1. Write each of the following numbers in its standard form.a) one and eighty-four thousandthsb) fi ve hundred two and thirteen hundredthsc) twelve and one hundred two thousandthsd) seventy-six ten thousandths

2. Write each of the following numbers in words.a) 0.408b) 1502.07c) 94.0036d) 8.020

3. List in order from smallest to largest.1.056, 1.06, 10.005, 1.5, 1.504

4. List in order from smallest to largest.0.61, 0.006, 0.0059, 0.0601, 0.0519

5. Order from largest to smallest.5.304, 5.043, 5.0043, 5.034, 5.0344

6. Round each of the following decimal numbers to the indicated place.a) Round 115.2354 to the nearest hundredth.b) Round 14.299 to the nearest hundredth.c) Round 8.398 to the nearest whole number.d) Round 0.6142 to the nearest thousandth.e) Round 43.0709 to the nearest tenth.f) Round 20.1095 to the nearest tenth.

ADDITIONAL EXERCISESADDITIONAL EXERCISES

Worked SolutionWhat is Wrong Here? Identify the Errors Correct Process

6) List in order from smallest to largest: 3.656, 3.67, 13.76, 3.1657

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Reading Assignment—Notes and Questions