Section 2.1
PRE-ACTIVITY
PREPARATION
Reading, Writing, Comparing,
and Rounding Decimal Numbers
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 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 fields 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.
LEARNING OBJECTIVES
•
Master reading and writing decimal numbers.
•
Put any set of decimal numbers in order.
•
Master the process of rounding a decimal number to a given decimal place value.
125
Chapter 2 — Decimal Numbers
126
TERMINOLOGY
PREVIOUSLY USED
NEW TERMS
TO
LEARN
base ten system
compare
decimal system
decimals
expanded form
decimal number
greater than symbol >
decimal places
less than symbol <
decimal place digit
midpoint
decimal point
number line
hundredths
place digit
hundred-thousandths
place value
order
round down
standard decimal notation
round up
tenths
standard form
ten-thousandths
thousandths
trailing zeros
BUILDING MATHEMATICAL LANGUAGE
From your study of whole numbers, you know that when you write a number in its standard form
in 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.”
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
127
The number 15.29 (“fifteen and twenty-nine hundredths”) is positioned properly in the chart below.
Place
name
Thousands
Hundreds
Tens
Ones
.
Tenths
Place
value
1000
100
10
1
.
.1
.01
1
5
.
2
9
Example
number
Hundredths Thousandths
.001
Ten-Thousandths
.0001
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:
1000
100
10
1
.1
.01
÷
÷
÷
÷
÷
÷
10
10
10
10
10
10
= 100
= 10
= 1
=
.1
=
.01
=
.001
one hundred
ten
one
one tenth
one hundredth
one thousandth, and so on as you move left to right in place value.
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:
10
10
10
10
10
10
×
.001
×
.01
×
.1
× 1
× 10
× 100
=
=
=
=
=
=
.01
.1
1
10
100
1000, and so on as you move left in place value
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 0.275
Both 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.
Chapter 2 — Decimal Numbers
128
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:
Dividing 1 into
10 equal parts
1
1
10
"one tenth"
.1
or
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.
1
100
"one hundredth"
.01
or
How might you visually represent .29
(twenty-nine hundredths) in the figure below?
How might you visually
represent .8 (eight tenths)
in the figure below?
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
129
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.
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
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.
2.10
2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20
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.”
Reading and Writing Decimal Numbers
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.
Chapter 2 — Decimal Numbers
130
TECHNIQUE
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 final digit
(farthest to the right).
Special
Case:
Zero (0) as the whole number
(see page 131, Model C)
MODELS
Translate each of the following numbers to its word form.
four hundred sixty-seven thousandths
Answer:
five hundred two and
four hundred sixty-seven thousandths
ten-thousandths
7
thousandths
thousandths
6
Step 2:
hundredths
hundredths
4
Step 2:
Step 1: ninety-one and
tenths
tenths
Step 1: five hundred two and
91.0815
.
B
►
502.467
.
A
►
0
8
1
5
eight hundred fifteen ten-thousandths
Answer:
ninety-one and
eight hundred fifteen ten-thousandths
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
Special Case: Zero (0) as the Whole Number
0.10275
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.
Step 1:
hundredths
thousandths
1
0
2
ten-thousandths
tenths
.
Step 2:
hundred-thousandths
C
►
7 5
Answer: ten thousand two hundred seventy-five hundred-thousandths
TECHNIQUE
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 final digit with the named decimal place value.
Step 3: Use a zero (0) placeholder if a decimal place is missing.
Special
Case:
No whole number part in the word form
(see page 133, Model D)
131
Chapter 2 — Decimal Numbers
132
MODELS
Translate each of the following numbers to its standard form.
Step 1: 406.
Step 2: twenty-one hundredths
hundredths
“four hundred six and twenty-one hundredths”
tenths
A
►
2
1
Step 3: all decimal places accounted for—
no zero decimal place holders needed.
Answer: 406.21
B
►
“ninety-four and two hundred seven hundred-thousandths”
Step 1: 94.
Step 3:
0 0 2
hundred-thousandths
ten-thousandths
thousandths
hundredths
tenths
Step 2: two hundred seven hundred-thousandths
0 7
zero placeholders for the missing decimal places
Answer: 94.00207
“three and fifty hundredths”
Step 2: fifty hundredths
Step 3: all decimal places accounted for
Answer: 3.50
hundredths
Step 1: 3.
tenths
C
►
5
0
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
133
Special Case: No Whole Number Part in the Word Form
D “eighty-three thousandths”
►
Step 1: 0.
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.
thousandths
0 8
3
tenths
hundredths
Step 2: eighty-three thousandths
Step 3: zero placeholders for the missing tenths place
Answer: 0.083
Comparing the Values of Decimal Numbers
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 by comparing their corresponding place values.
For example, which is smaller, 0 . 8 2 5 or 0 . 8 2 3 ?
same
same
different
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-five 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.
Chapter 2 — Decimal Numbers
134
METHODOLOGY
Comparing (Ordering) Decimal Numbers
Order the following list of numbers from smallest to largest.
►
►
Example 1: 3.25,
3.6,
Example 2: 6.219,
4.3,
5.201,
3,
3.384
6.3,
6.21,
6.02
Try It!
Steps in the Methodology
Step 1
List the
numbers.
Step 2
Sort by whole
numbers.
Write the numbers in a column, aligning
place values and decimal points.
Arrange the numbers in the desired
order (smallest to largest or largest
to smallest) according to their whole
numbers (ignoring the decimal
places).
Example 1
Example 2
3.25
3.6
4.3
3.
3.384
smallest to largest
Rank
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.
?????
Why can and why do you do this?
Special
Case:
Step 4
Order by
fractional
parts.
Two or more whole number
sets to order in the list
(see page 135, Model)
Order the set according to the fractional
parts.
THINK
0 < 250 < 384 < 600
Step 5
Present the
answer.
Write the original numbers in the
correct order.
5
Rank
3.25
3.250
3.6
3.600
3.
3.000
3.384
3.384
4.3
4.3
5
3.25
3.250
Rank
2
3.6
3.600
4
3.
3.000
1
3.384
3.384
3
4.3
4.3
5
3, 3.25, 3.384, 3.6, 4.3
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
135
?????
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
MODEL
Special Case: Two or More Whole Number Sets to Order in the List
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
Step 1
1.7087
0.078
0.87
1.781
0.0877
0.8
largest to smallest
1.7087
1.781
0.078
0.87
0.0877
0.8
} set of numbers with 1 as the whole number
}
set of numbers with 0 as the whole number
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 final order.
Steps 3 & 4
Step 5
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
THINK
7810 > 7087
THINK
8700 > 8000 > 877 > 780
Answer: 1.781, 1.7087, 0.87, 0.8, 0.0877, 0.078
Chapter 2 — Decimal Numbers
136
Rounding Decimal Numbers
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 specified decimal place as the decimal place digit.
METHODOLOGY
Rounding a Decimal Number
►
►
Example 1: Round 43.9738 to the nearest hundredth.
Example 2: Round 24.61809 to the nearest thousandths place.
Steps in the Methodology
Step 1
Determine
final number
of decimal
places.
Step 2
Identify the
place digit.
Determine the number of decimal
places in the final answer.
???
Why do you do this?
Identify the digit in the specified place
value (the place digit) by marking it
with an arrow.
Special
Case:
Step 3
Identify the
digit to the
right of the
place digit.
Step 4
Compare to
the number 5.
Step 5
Round up or
down.
Rounding to the nearest
whole number
(see page 138, Model 1)
Identify the digit occupying the decimal
place immediately to the right of the
place digit by circling it.
Determine whether the circled digit is
less than, equal to, or greater than 5.
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.
Try It!
Example 1
hundredth
The final answer
will have two
decimal places.
43.9738
43.9738
3<5
The hundredths place
digit does not change
43.97xx
Example 2
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
Steps in the Methodology
Step 6
Present the
answer.
137
Example 1
Example 2
To present your answer, drop all
decimal place digits to the right of the
specified place value.
???
Why can you do this?
43.97
Presenting a zero in the
Special
specified place value
Case:
(see page 138, Model 2)
???
Why do you do Step 1?
The last decimal place value for a rounded answer will always be named, so the final answer must have only
as many decimal places as specified to reflect the corresponding fractional part.
In Example 1, the named hundredths place requires two and only two places to the right of the decimal point.
???
Why can you do Step 6?
As the result of rounding, the digits to the right of the specified 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.
Chapter 2 — Decimal Numbers
138
MODELS
Model 1
Special Case: Rounding to the Nearest Whole Number
Round 246.547 to the nearest whole number.
Rounding to the nearest whole number means rounding to the ones place.
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
246.547
Pictured on a number line:
246
246.5
247
midpoint
Model 2
Special Case: Presenting a Zero in the Specified Place Value
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
Pictured on a number line:
12.3997
12.39
12.395
midpoint
12.40
After rounding up or down, if the specified
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.
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
139
ADDRESSING COMMON ERRORS
36.052
read as
52 is re
52
“thirty-six
hi y-s x and
fifty-two
hundredths”
wo h
und
und
Correct Process
Use the place value
chart and align the
digits with the chart.
36. 0
thousandths
Reading decimal
numbers
incorrectly when
there are zeros
as decimal place
holders in the
standard form
Resolution
hundredths
Incorrect Process
tenths
Issue
5 2
36.052 is read as
“thirty-six and
fifty-two thousandths”
Comparing
without regard
to decimal place
values
Compare:
4.0387 and 4.38
THINK
387 > 38
4.0387
4.0387
4.0
is larger
a er tthan
h
4.38
4 38
Incorrectly
identifying
decimal places
when rounding
Round 87.6349 to the
nearest hundredth.
Thinking, “ones,
tenths, hundredths
… the 4 is in the
hundredths’ place.”
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.
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.
Compare:
4.0387 and 4.38
4.0387
4.38
THINK
4.0387
4.3800
3800 > 387
3800 ten-thousandths >
387 ten-thousandths
Therefore,
4.38 > 4.0387
In 87.6349, the 3 is in
the hundredths place.
87.6349
Answer: 87.63
87.6349
87
7.6 49
Answer:
87.635
we 87
8
7
Incorrectly
presenting the
final rounded
decimal number
917
1
179
ro
32.9179
rounded
e tent
s place
to the
tenths
s 32.9000
3 90
90
is
Rounding decimals
requires dropping the
digits to the right of the
specified 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
Chapter 2 — Decimal Numbers
140
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.
When rounding to a
designated place value,
the final answer must
present the specified
number of decimal
places to indicate that
level of accuracy.
Round 73.0348 to the
nearest tenth.
73.0348
3 .0348
3.0
Answer:
73
swer: 7
Rounding to tenths means
there must be one decimal
place in the final answer.
73.0348 rounded to the
nearest tenth
is 73.0
PREPARATION INVENTORY
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 identification 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
Section 2.1
ACTIVITY
Reading, Writing, Comparing,
and Rounding Decimal Numbers
PERFORMANCE CRITERIA
• Translating between standard decimal notation and words
– correct identification 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 specified place values
– correct identification of the specified place value
– consistent documentation and presentation with appropriate notation
– accuracy in the rounding process
CRITICAL THINKING QUESTIONS
1. What are three real-world situations that use decimal numbers?
•
•
•
2. How is the whole number part separated from the decimal fraction part in reading and writing a decimal
number?
141
142
Chapter 2 — 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?
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
143
8. How can you make sure that you order a set of decimal numbers correctly?
9. What is the most significant difference between rounding whole numbers and rounding decimal numbers?
10. When would you present a zero (0) as the final decimal place digit in a rounded answer?
11. In the U.S. monetary system, why are dollar amounts rounded to two decimal places?
Chapter 2 — Decimal Numbers
144
TIPS
FOR
SUCCESS
• 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.
DEMONSTRATE YOUR UNDERSTANDING
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 _________________________________________________________________
_________________________________________________________________
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
4. Order the following numbers from smallest to largest: 2.046, 2.4, 1.06, 2, 2.46
Worked solution:
Answer:
5. Order the following numbers from smallest to largest: 24.07, 24.007, 24.005, 24.058, 24.0059
Worked solution:
Answer:
6. Order the following numbers from largest to smallest: 0.05, 1.03, 1.9, 0.1, 0.201
Worked solution:
Answer:
145
Chapter 2 — Decimal Numbers
146
7. Round 713.54973 to the indicated place.
713.54973
Rounding Process
Answer
a) tenth
b) hundredth
c) thousandth
d) tenthousandth
e) hundred
f) nearest whole
number
TEAM EXERCISES
1. In the grids below, fill in the correct number of rectangles to represent the following decimal numbers.
(Hint: you may find 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?
Section 2.1 — Reading, Writing, Comparing, and Rounding Decimal Numbers
2. List fifteen decimal numbers between 0.25 and 0.26
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147
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IDENTIFY
AND
CORRECT
THE
ERRORS
Identify and correct the errors 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?
1) Round 62.3585 to the nearest
hundredth.
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.
Identify the Errors
Rounded to the
thousandths place,
not the specified
hundredths place.
Correct Process
62.3585
Answer: 62.36
Chapter 2 — Decimal Numbers
148
Worked Solution
What is Wrong Here?
Identify the Errors
6) List in order from smallest to largest:
3.656, 3.67, 13.76, 3.1657
ADDITIONAL EXERCISES
1. Write each of the following numbers in its standard form.
a) one and eighty-four thousandths
b) five hundred two and thirteen hundredths
c) twelve and one hundred two thousandths
d) seventy-six ten-thousandths
2. Write each of the following numbers in words.
a) 0.408
b) 1502.07
c) 94.0036
d) 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.
Correct Process