Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Tenths, Hundredths, and
Thousandths
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
______________________________________________________
2. In a place value grid, each place is ______ times greater than the
next place to its ________ .
3. In a place value grid, each place value equals the place value to
its left divided by _________.
b. 10 4 10 5 1
100 3
10 3
5 _____
1
}}
10
of the value of
© Riverdeep, Inc.
¥ Use a place value
grid to explore
1-place decimal
numbers.
¥ Represent
hundredths and
thousandths in
standard form,
expanded form,
and word form.
?
ne
s
O
s
Te
n
H
un
dr
ed
s
the place directly to its _________ .
6. Use the place value grid to
complete parts a and b.
Learning
Objectives:
¥ Use a place value
grid to explore
2- and 3-place
decimal numbers.
5 _____
5. In a place value grid, the value of a place is
Fraction
Decimal
Decimal point (.)
Tenth
Hundredth
Thousandth
Reciprocal
¥ Represent tenths
in standard form,
expanded form,
and word form.
4. Write each division as a multiplication.
a. 100 4 10 5 10
Key Words:
a. Complete the expressions
we can use to find the
value of the shaded place.
_____ 4 _____ 5 _____
_____ 3 _____ 5 _____
b. Since these expressions are both equal to _____ , the
highlighted place must be the __________ place.
Destination
Math
121
Name ___________________________________
Date ________________________
7. The point in a decimal number is used to separate the
__________ ____________ part and the _______________ part
of a number.
a. What fraction represents the
value of the place to the right
0
8.
35
6
th
s
Te
n
ne
s
2
O
H
un
dr
s
ed
s
9. Use the place value grid to
complete parts a and b.
Te
n
35
35
7.
7.
0
5
8. Label the number line using decimal numbers to the tenths place.
2
4
0
7
of the tenths place?________ Label the place on the place value grid.
b. What fraction represents the value of the next unlabeled place?
__________ Label the place on the place value grid.
10. Use the number 622.407 for parts a and b.
a. Write the value of each place as the product of factors.
(6 3 _____ ) 1 (2 3 _____ ) 1 ( _____ 3 1) 1
) 1 ( _____ 3
) 1 ( _____ 3
© Riverdeep, Inc.
( _____ 3
)
b. Find the products in part a to show the number in expanded form.
_____ 1 _____ 1 _____ 1
1
11. Write the word name for 622.407. __________________________
______________________________________________________
Destination
Math
122
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Tenths, Hundredths, and
Thousandths
1. Use the place value grid
to complete parts aÐc.
a. Label each place on
the place value grid.
b. Write the number two hundred sixty-one and four tenths on
the grid.
c. Express this number as a mixed number in lowest terms.
____________
2. Write each mixed number as a decimal number.
a. 16 }13}0 5 _________
c.
9
}}
10
5 _________
b. 271 5}3} 5 _________
d. 34 2}1} 5 _________
3. Write each decimal number in expanded form. Then write the
word name of each number.
a. 9.1 5 ____________
Word name __________________________________________
b. 183.7 5 _________________________
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Word name __________________________________________
____________________________________________________
c. 40.2 5 ______________
Word name __________________________________________
Destination
Math
123
th
Te
n
O
ne
s
Te
n
s
s
ed
dr
un
H
4. Use the place value grid
to complete parts a and b.
Date ________________________
s
Name ___________________________________
a. Label the two unlabeled
places on the place
value grid.
b. Write 36.095 on the grid.
5. Write each mixed number as a decimal number.
25
418
7
} 5 __________ b. 73 }} 5 __________ c. 1}} 5 __________
a. 6 }
100
1,000
100
6. Write each decimal number in expanded form. Then write the
word name of each number.
a. 249.62 5 ______________________________
Word name __________________________________________
b. 5.088 5 ______________________________
Word name __________________________________________
7. Complete the expanded form of this mystery number using the
following statements. 9 1 _____ 1
3
}}
100
1_____
© Riverdeep, Inc.
¥ The digit in the tenths place is a prime number that is less than
the digit in the hundredths place.
¥ The sum of the digits to the right of the decimal point equals the
value of the digit in the ones place.
Now write the mystery number in standard form. __________
Destination
Math
124
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Ordering and Rounding
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
______________________________________________________
2. Since each of the record times shown has a digit in the
________________ place, we can round each number to the
Key Words:
Bar graph
Data
Learning
Objectives:
¥ Round decimals to
the nearest tenth.
¥ Represent data on
a bar graph.
¥ Compare and order
two or more
decimals.
nearest ________ .
3. Help Dijit round 11.10 to the nearest tenth.
a. The decimal _____ and the fraction _____ both represent
_____ hundredths.
b. Since
10
}}
100
5
3
, 0.10 5 _____ .
c. The number 11.10 can be written as _____ .
4. When rounding to the nearest tenth, look at the value of the digit
in the ________________ place.
5. Round each number to the nearest tenth.
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a.10.587 < ________
b.10.459 < ________
c.10.345 < ________
Destination
Math
125
Name ___________________________________
Date ________________________
6. Use the bar graph to complete parts aÐd.
Year
1956
1961
1987
1989
1990
0 10.0
10.3
10.6
11.1
10.5
a. What does the symbol
11.0
Time (s)
12.0
represent? ________________________
____________________________________________________
b. A ______ ___________ uses vertical or horizontal bars to represent
information, or ___________ .
c. Complete the bar graph by drawing a horizontal bar for each year.
d. What does the data on the bar graph tell us about the record
times? ______________________________________________
7. To order and compare decimals:
¥ Arrange the numbers in a __________ ____________ grid.
© Riverdeep, Inc.
¥ Start by comparing the digits in the greatest place to the
____________ of the decimal point.
¥ Moving to the ___________ , compare the values of the digits in the
___________________ places.
Destination
Math
126
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Ordering and Rounding
1. Round each number to the nearest tenth.
a. 62.58 < _______ b. 7.139 < _______
c. 81.964 < _______
2. The chart shows the areas of four countries in millions of square
kilometers.
Country
Area
Iran
1.65
Mali
1.24
Mongolia
1.57
Peru
1.29
Rounded Value
a. Round each number to the nearest tenth, and write each value
in the chart.
b. Plot and label each rounded number on the number line.
© Riverdeep, Inc.
Country
0
1
1.5
2
2
Area (million km )
c. Starting with the country that has the largest area, write the
names of the countries in order under the heading ÒCountry.Ó
d. Use the bar lines to the right of each countryÕs name to draw
a horizontal bar that represents the countryÕs area.
(Hint: Where should each bar stop?)
Destination
Math
127
1.324
1.17
1.503
hs
dt
th
sa
n
ed
Th
ou
dr
H
un
s
th
Te
n
s
O
ne
3. Use the place value grid to order
this set of numbers from least (top)
to greatest (bottom).
Date ________________________
s
Name ___________________________________
1.21
Which place did you compare?
_______________
4. Order each set of numbers from least to greatest.
a. 16.78 16.59
16.9
16.52 ______ , ______ , ______ , ______
b. 7.19
7.148
7.031 ______ , ______ , ______ , ______
7.035
5. The table shows the times, in seconds, for swimmers from five
different countries who competed in a 50-meter freestyle race.
Country
Time (s)
Brazil
22.92
Germany
22.73
Great Britain
23.01
Italy
22.96
Netherlands
22.67
Country
Time (s)
© Riverdeep, Inc.
a. Reorder the data in the table at the left so that the times are from
least (top) to greatest (bottom).
b. The fastest swimmer came from which country? ____________
Explain. ____________________________________________
____________________________________________________
Destination
Math
128
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Ratios, Decimals, and
Percents
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
______________________________________________________
50,000
}}
100,000
5
100
40,000
} 5
b. }
100,000
100
10,000
} 5
c. }
100,000
Ratio
Percent
Circle graph
Bar graph
Learning
Objectives:
2. Write each of these fractions as equivalent fractions with
denominators of 100.
a.
Key Words:
¥ Express ratios
as percents.
100
3. These equivalent fractions tell us that if the bear population in
Alaska were 100, there would be ______ black bears,
¥ Express a decimal
as a percent.
¥ Express the
equivalences
among ratios,
decimals, and
percents.
______ brown bears, and ______ polar bears.
4. Write the fraction that represents each type of fruit in the group of
10 fruits.
a. Bananas ______
b. Apples ______
c. Lemons ______
5. Out of 10 fruits, ______ are yellow and ______ are green. The
fractions ______ and ______ describe the fruits when they are
© Riverdeep, Inc.
arranged by ____________ .
6. A __________ is a fraction that compares ________ quantities.
7. A ____________ is a ratio between a number and
_____ _____________ . What symbol do we use to represent
a percent? _____
100
} as a percent. _____
8. Express the ratio 1}
00
Destination
Math
129
Name ___________________________________
Date ________________________
9. We can write a fraction with a denominator of 100 as a percent by
writing _____ beside the _________________ .
10. Write the four ways shown on the circle graph that describe the
ratio of black bears to the total population of bears.
______________
______________
_____
_____
11. The diet of a typical bear is _____ nuts and berries, _____ insects,
_____ meat and fish, and _____ plants.
12. To write a fraction as a ______________ , first express the
fraction as an ______________ fraction in ________________ .
13. Write each fraction as an equivalent fraction in hundredths. Then
write each fraction as a percent.
a.
1
}}
2
5
100
5 _____
b.
1
}}
10
5
100
5 _____
c.
1
}}
4
5
100
5 _____
d.
3
}}
20
5
100
5 _____
14. What percent represents a bearÕs total diet? _________
15. Express each fraction as a decimal in hundredths.
50
}}
100
5 _____
10
} 5 _____
b. }
100
25
15
} 5 _____ d. }} 5 _____
c. }
100
100
© Riverdeep, Inc.
a.
16. Write the four ways shown on the bar graph that express the ratio
of meat and fish in a bearÕs diet to a bearÕs total diet.
_____
_____
_____
_____
Destination
Math
130
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Ratios, Decimals, and
Percents
1. Write each fraction as an equivalent fraction with a denominator
of 100. Then write each fraction as a percent.
5
100
5 ________
b.
3
}}
4
5
100
5 ________
18,000
}5
c. }
100,000
100
5 ________
d.
2
}}
5
5
100
5 ________
13
}}
20
100
5 ________
3,600
}5
f. }
10,000
100
5 ________
a.
e.
670
}}
1,000
5
2. The circle graph shows the number of
balloons of each color in a package
of 25 balloons. Use this information
to complete the chart below. Show
the ratios both as a fraction of the total
and as a fraction with a denominator
of 100.
Balloon Color
Ratio of Color to Total
Blue
3
Red
9
Green
6
Yellow
7
Percent of Total
Blue
Green
Red
© Riverdeep, Inc.
Yellow
3. Write each decimal as a fraction with a denominator of 100. Then
write each decimal as a percent.
a. 0.38 5
100
5 ________
b. 0.60 5
100
5 ________
c. 0.17 5
100
5 ________
d. 0.05 5
100
5 ________
e. 0.99 5
100
5 ________
f. 0.26 5
100
5 ________
Destination
Math
131
Name ___________________________________
Date ________________________
4. Use equivalent fractions, decimals, and percents to complete the
chart below.
Fraction (Ratio)
Decimal
Percent
9
}}
20
0.21
7%
0.50
17
}}
25
5. Sally tossed a coin 50 times. Of these tosses, 56% showed heads
and 44% showed tails.
a. How many of the tosses showed heads? _____ How many of
the tosses showed tails? _____
b. Use the bar graph to show how many of the tosses showed
heads and how many showed tails.
Toss
Heads
Tails
20
25
© Riverdeep, Inc.
0
30
Number of Tosses
Destination
Math
132
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
Tenths, Hundredths, and Thousandths
1. Write each mixed number as a decimal number.
a. 21 }17}0 5 ________
59
} 5 ________
b. 6 }
1,000
c. 430 5}2} 5 ________
66
} 5 ________
d. 92 }
100
2. Write each decimal number in expanded form. Then write the word
name of each number.
a. 527.31 5 ____________________________________________
Word name __________________________________________
b. 60.202 5 ____________________________________________
Word name __________________________________________
Ordering and Rounding
3. Round each number to the nearest tenth.
a. 18.37 < ________
b. 0.626 < ________
4. Order this set of numbers from least to greatest.
0.76
0.613
0.72
0.63
0.706
© Riverdeep, Inc.
_________ , _________ , _________ , _________ , _________
Ratios, Decimals, and Percents
5. Use equivalent
fractions, decimals,
and percents to
complete the chart.
Fraction (Ratio)
Decimal
Percent
0.03
14
}}
25
82%
Destination
Math
133
Name ___________________________________
Date ________________________
Putting It All Together
6. The chart shows the
times, in seconds, in
which four students
ran a 200 m race.
a. Order the times from
least to greatest.
Name
Time (s)
Maria
23.08
Jamel
23.41
Seth
23.25
Katie
23.49
Rounded Time (s)
____________ , ____________ , ____________ , ____________
b. Round each time to the nearest tenth, and write the values in the
chart.
c. Represent
each rounded
value on the
bar graph in
order from
least to
greatest.
Name
0
23
23.5
24
Time (s)
© Riverdeep, Inc.
7. A bouquet of 20 flowers contains 10 snapdragons, 8 daisies, and
2 sunflowers.
a. Each type of flower makes up what percent of the bouquet?
Snapdragons ______
Daisies ______
Sunflowers ______
b. What fraction of the bouquet is each kind of flower? Express your
answers in lowest terms.
Snapdragons ______
Daisies ______
Sunflowers ______
Destination
Math
134
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 4: Decimals
UNIT 1: Introduction
1. The United States menÕs relay team won the Silver Medal in the
5
} seconds.
1996 Olympic 400-m relay. Their winning time was 38 }
100
a. Label each place in the place value grid.
5
} as a decimal number in the grid.
b. Write 38 }
100
5
} in expanded form. __________________________
c. Write 38 }
100
5
}. __________________________
d. Write the word name of 38 }
100
2. The chart shows
the average winning
race-car speed for
four years of the
Indianapolis 500.
Year
Speed (mph)
1972
162.962
1977
161.331
1978
161.363
1982
162.029
Rounded Speed (mph)
a. Order the speeds from least to greatest.
____________ , ____________ , ____________ , ____________
© Riverdeep, Inc.
b. Round each value to the nearest tenth, and write the values in
the chart.
c. Represent
each
rounded
value on
the bar
graph.
Year
1972
1977
1978
1982
0
161 161.2 161.4 161.6 161.8 162 162.2 162.4 162.6 162.8 163
Speed (mph)
Destination
Math
135
Name ___________________________________
3. Marla counts 20 books on one of
her bookshelves. The circle graph
shows the number of each type
of book on the shelf.
Date ________________________
Poetry
2
Humor
4
a. Write a ratio to represent each
type of book in the group. Then
write each ratio as an equivalent
fraction with a denominator
of 100.
Fiction
9
Nonfiction
5
Fiction ________ 5 _____
Humor ________ 5 _____
Nonfiction ________ 5 _____
Poetry ________ 5 _____
b. What percent of the books is nonfiction? _____
c. What percent of the books is poetry? _____
d. What type of book does the decimal
number 0.45 represent? __________
4. Bentucket Middle School has about 1,000 students. The percent
of students in each grade are: sixth graders, 38%; seventh graders,
33%; and eighth graders, 29%. About how many students are in
each grade? Show your work.
Sixth grade _____
Seventh grade _____
Eighth grade _____
© Riverdeep, Inc.
Destination
Math
136