Download Place Value Through Billions

Name _____________________________________________________________________________________________________
Place Value Through Billions
R 1-1
Pluto is the ninth planet in our solar system. It orbits the sun at an average
distance of 3,666,370,000 miles.
Ones
3,
6
6
6,
3
7
0,
0
0
es
Thousands
on
Millions
hu
bil ndre
lio
d
tenns
bil
lio
ns
bil
lio
ns
hu
mi ndre
llio d
ten ns
mi
llio
ns
mi
llio
ns
hu
tho ndre
us d
ten ands
tho
us
a
tho nds
us
an
ds
hu
nd
re d
s
ten
s
Billions
0
Note that the 0 in the thousands, hundreds, tens, and ones places holds
the place for these numbers. Its value is zero.
Write each number in the place value chart. Then give the value of the underlined digit.
Ones
es
Thousands
on
Millions
hu
bil ndre
lio
d
tenns
bil
lio
ns
bil
lio
ns
hu
mi ndre
llio d
ten ns
mi
llio
ns
mi
llio
ns
hu
tho ndre
us d
ten ands
tho
us
a
tho nds
us
an
ds
hu
nd
red
s
ten
s
Billions
1. 4,510,773,000
4
5
1
0
7
7
3
0
0
0
2. 2,405,986
3. 35,110,297,420
4. 1,256,000,398
© Scott Foresman, Gr. 5
(1)
Use with Chapter 1, Lesson 1.
Name _____________________________________________________________________________________________________
Place Value Through Billions
H 1-1
Write the value of each underlined digit.
1.
526,331
2.
62,989,100
3.
909,781,425
Give the value of the digit 7 in each number.
4.
213,784,219,906
5.
$6,579,002,495
Write each number in expanded form.
6.
$32,120
7.
960,322
8.
44,650
9.
7,368,911
Write each number in standard form.
10.
What is the greatest number you can make using all of the digits from
0 through 9 exactly once?
11.
What is the least number you can make using all of the digits from
0 through 9 exactly once?
Test Prep Circle the correct letter for each answer.
12. 7,000,000 is read
13. In 324,781, the value of 3 is
A 7 thousand
F 3 thousand
B 7 million
G 3 hundred
C 7 hundred
H 3 hundred thousand
D 70 million
J 30 thousand
© Scott Foresman, Gr. 5
(2)
Use with Chapter 1, Lesson 1.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
R 1-2
Exact and Estimated Data
Exact data will show an amount that can be counted, even if it is difficult to count.
Estimated data are numbers that have been rounded or that represent numbers
that cannot be measured or counted.
Here are some examples of exact and estimated data.
Exact data
Last year, Jim saw 2 comets.
Estimated data
The Sun is about 93,000,000
miles from Earth.
Apollo 13 was launched in 1970.
After the Sun, the nearest star
is about 4 light-years away.
Many of the 88 constellations were named by the ancient Greeks and Romans
after characters from mythology. One ancient Greek tale gave us the names
for 5 constellations: Perseus, Andromeda, Pegasus, Cassiopeia, and Cepheus.
Within the star group Andromeda, you can see an entire galaxy of stars, the
Andromeda Nebula. This galaxy is about 2 million light-years away from Earth.
It is the most distant object you can see without binoculars or a telescope.
Work with a partner to solve.
1. How many constellations’ names came from a single ancient Greek tale?
2. Is this number an exact number or an estimate? Explain your answer.
3. Give an example of another exact number from the reading above.
4. Is about 2 million light-years an exact number or an estimated number? Explain.
5. Is the number of stars in an entire galaxy an estimated or an exact number? Explain.
© Scott Foresman, Gr. 5
(4)
Use with Chapter 1, Lesson 2.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
H 1-2
Exact and Estimated Data
For exercises 1–3, circle the correct letter of the answer.
Some scientists believe the solar system may hold an undiscovered 10th planet—Planet X.
They estimate that the planet would have a mass of 2 to 5 times that of Earth. It would
have to orbit between about 4.65 billion and 9.3 billion miles from the sun.
1. Which of these numbers is exact?
a. 10th planet
b. 4.65 billion miles
c. 9.3 billion miles
2. Pluto orbits about 3.66 billion miles from the sun.
If Planet X exists, about how close might it come to Pluto?
a. exactly 1 billion miles
b. about 1 billion miles
c. much more than 1 billion miles
3. Where are astronomers searching for Planet X?
a. at an orbit 4.65 billion miles from the sun
b. at an orbit 9.3 billion miles from the sun
c. in an orbit ranging from 4.65 billion to 9.3 billion miles from the sun
The distances between the sun and the planets are greater than most people realize.
For instance, Pluto is about 3.66 billion miles from the sun. This means that if you
made a model of Pluto that was the size of a quarter, the model of the sun would
need to be 38 feet wide and placed about 31 miles away.
4. Which of the numbers above are estimates? Explain how you know.
5. If you also made a coin-sized model of Planet X, and you used the model of the sun
that is 38 feet wide, how far from Planet X would you need to place the sun?
a. less than 31 miles away
b. exactly 31 miles away
c. more than 31 miles away
6. Give an example of an exact number from the reading above?
© Scott Foresman, Gr. 5
(5)
Use with Chapter 1, Lesson 2.
Name _____________________________________________________________________________________________________
Place Value Through Thousandths
R 1-3
Comet Halley visits Earth about once every 76 years. Comet Brorsen visits Earth
every 5.463 years.
You can read and write 5.463 and other decimals in word form.
Standard Form
Word Form
Short Word Form
5.463
five and four hundred sixtythree thousandths
5 and 463 thousandths
5.46
five and forty-six hundredths
5 and 46 hundredths
5.4
five and four tenths
5 and 4 tenths
To write a decimal using words:
• Write the whole number part.
• Write and for the decimal point.
• Write the decimal part to the last place given.
Show each number in the place-value chart or write the number in word form. The first
one is done for you.
3
6
5 . 4
3
s
dth
four tenths
____________________________________________________
7 . 0
0
two and two hundred thirty-six thousandths
____________________________________________________
____________________________________________________
.
2
us
an
tho
dre
ten
ths
es
hu
n
1
2 . 2
on
s
ten
hu
n
dre
ds
dth
s
Ones
9
____________________________________________________
.
forty-two and three hundred five thousandths
____________________________________________________
6 . 8
____________________________________________________
.
four and twenty-three hundredths
____________________________________________________
5 . 1
8
6
____________________________________________________
____________________________________________________
© Scott Foresman, Gr. 5
(7)
Use with Chapter 1, Lesson 3.
Name _____________________________________________________________________________________________________
Place Value Through Thousandths
H 1-3
Write each number in standard form.
1. three and eighteen hundredths
2. four and two hundred three thousandths
3. thirty-eight thousandths
4. one hundred seventy-seven thousandths
5. three and twenty-four hundredths
6. sixty and sixty-one thousandths
Write the word name for each decimal.
7. 7.45
8. 0.061
9. 9.04
10. 21.046
11. 7.743
12. 0.045
Draw a line from the clue to the decimal.
13. I have a 3 in my hundredths place. I am less than 1.
1.739
14. I am greater than 2. All of my digits are odd.
0.138
15. I am less than 2. I have a 9 in my thousandths place.
1.234
16. I am more than 1. My digits increase from left to right.
3.513
Test Prep Circle the correct letter for each answer.
17. What is the value of the underlined
digit? 2.348
18. What digit is in the thousandths place?
1,432.789
A hundreds
C tens
F 4
H 2
B tenths
D hundredths
G 9
J 8
© Scott Foresman, Gr. 5
(8)
Use with Chapter 1, Lesson 3.
Name _____________________________________________________________________________________________________
Comparing and Ordering Whole Numbers
and Decimals
R 1-4
The four brightest stars we can see are Sirius, Canopus, Proxima Centauri and
Alpha Centauri. The distance to Sirius is 8.6 light years. It’s 98.0 light years to
Canopus. Proxima Centauri is 4.24, and Alpha Centauri is 4.34 light years away.
Which is farthest away? Compare the numbers.
Step 1 Write the
Step 2 Compare the digits Step 3 Continue
numbers so they
in the same place.
comparing until
line up on the
Start at the greatest
the digits differ.
decimal point.
place.
nd
tho redth
s
us
an
dth
s
ths
8 . 6
8 . 6
8 . 6
9 8 . 0
9 8 . 0
9 8 . 0
hu
ten
nd
r
ten eds
s
on
es
hu
ths
hu
ten
hu
nd
r
ten eds
s
on
es
nd
tho redth
s
us
an
dth
s
ths
hu
ten
nd
r
ten eds
s
on
es
hu
Ones
nd
tho redth
s
us
an
dth
s
Ones
Ones
4 . 2 4
4 . 2 4
4 . 2 4
4 . 3 4
4 . 3 4
4 . 3 4
9 tens is the
greatest number.
98.0 > 8.6 >4.34
>4.24
Canopus is farthest away. Proxima Centauri is closest.
dth
s
us
an
tho
red
hu
nd
ths
ten
es
ths
Ones
on
345.678; 5.111; 1,345.79;
0.515
Thousands
hu
tho ndre
us d
ten ands
tho
us
a
tho nds
us
an
ds
hu
nd
red
s
ten
s
In the place-value chart, write the
numbers in order from greatest
to least.
.
.
.
.
© Scott Foresman, Gr. 5
(10)
Use with Chapter 1, Lesson 4.
Name _____________________________________________________________________________________________________
Comparing and Ordering Whole Numbers
and Decimals
H 1-4
Write the numbers in order from least to greatest.
1. 2,000,000; 20,000,000; 12,000,000
2. 723,219; 723,319; 7,323,119
3. 44.882; 44.812; 44.810
4. 87.59; 875.9; 8.759
5. 76,844; 76,844.10; 76,844.101
6. 4,513.91; 4,313.91; 4,531.991
7. 1,335.803; 1,305.803; 1,305.830
8. 73.121; 73.212; 73.211
9. Each square contains a number from Exercises 1–8.
Shade each square
that contains the least
number in that exercise.
The remaining squares
will spell out the name
of a planet with
a 29-day year.
1
12,000,000
S
2
723,219
M
3
44.882
A
4
87.59
T
5
76,844.101
U
6
4,513.91
R
7
1,335.803
N
8
73.121
H
Test Prep Choose the correct letter for each answer.
10. 1,216,506
A
! 216,506
>
© Scott Foresman, Gr. 5
B <
(11)
C =
11. 4.37
F
! 4.73
>
G <
H =
Use with Chapter 1, Lesson 4.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
R 1-5
Draw a Diagram
A dog is pulling a sled up a 25-foot hill. It
slides back 2 feet for every 9 feet it climbs.
How many feet will the dog actually move
upward to reach the top of the hill?
Understand What data do
you have? The hill is 25 feet
high. The dog slides back 2
feet for every 9 feet it climbs.
Plan You can make a diagram.
Solve First: The dog climbs 9 feet, slides back 2 feet. It is 7 feet up the hill.
Second: The dog climbs 9 feet, then slides back 2 feet, so it climbs another 7
feet. Since 7 ! 7 " 14, the dog is now 14 feet up the hill.
Third: The dog is now 21 feet up the hill, because 14 ! 7 " 21.
Fourth: The dog climbs 4 feet and reaches the top, because 21 ! 4 " 25.
But altogether, the dog climbs: 9 ft ! 9 ft ! 9 ft ! 4 ft " 31 ft.
Look Back Does the diagram fit the facts?
Draw a diagram to solve the problems.
1. A frog jumps 6 hops forward, then 2 hops back. How many hops forward will it take
him to go 15 hops?
a. After 6 hops forward, the frog travels
b. After 12 hops forward, the frog travels
hops.
!!
!
!!!!!
hops.
c. How many hops forward will it take the frog to go forward 15 hops?
hops
2. Alissa built a kaleidoscope from two tubes. One tube is twice as long as the other. The
short tube extends out by 3 inches when 1 inch of it is fitted inside the long tube. The
finished kaleidoscope is 11 inches long. How long is each tube?
© Scott Foresman, Gr. 5
(13)
Use with Chapter 1, Lesson 5.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
H 1-5
Draw a Diagram
Draw a diagram on a separate sheet of paper to solve each problem.
1. In a dance, every time Nan takes 9 steps forward, she must take
3 steps back. The other side of the stage is 22 steps away. How
many steps will Nan actually take forward before she is in the offstage area?
2. Matt built a kaleidoscope from two tubes. One tube is twice as long as the
other. Half of the short tube is pushed inside the long tube. 4 cm of the short tube
extends out. The finished kaleidoscope is 20 cm long. How long is each tube?
wide and 2!12! inches high. The editor wants to publish
them in rows across the page. Each page is 8!12! inches
wide and 11 inches long. The photos should not touch
each other, and there should be about 1 inch of space
at each edge of the page. How many photos can she
use per row? Explain.
! in.
2!1
2
3. The school newspaper has photos that are 2 inches
2 in.
4. Two climbers are hiking up a 3,000-ft mountain. Each day they climb 1,000 ft and then
come down 250 ft to make camp. How many days will it take them to reach the top?
5. If a rock climber slides down 2 ft every 13 feet she climbs, how many feet will she
actually climb to reach a height of 36 feet?
© Scott Foresman, Gr. 5
(14)
Use with Chapter 1, Lesson 5.
Name _____________________________________________________________________________________________________
Rounding Whole Numbers and Decimals
R 1-6
Round 689 to the nearest hundred. Round 0.138 to the nearest tenth.
(8 rounds up)
(3 rounds down)
689
0.138
!"
!"
!"
!"
To round up, increase the
underlined digit by 1. To round
down, leave the underlined digit
alone. If you are rounding a
whole number, change all the
digits to the right of the
underlined digit to 0. If you are
rounding a decimal, you do not
need to add zeros.
0.138
!"
!"
!"
Step 3
689
!"
Look at the digit to the right.
Round up if it is 5, 6, 7, 8, or 9.
Round down if it is 0, 1, 2, 3, or 4.
0.138
!"
Step 2
689
!"
Underline the digit of the place you
are rounding to.
!"
Step 1
700
0.1
Write up if you should round up. Write down if you should round down. Then round each
number to the place named.
Number
up or down
nearest ten
Number
down
470
4. 0.371
1. 472
2. 39,829
5. 6.121
3. 15,260
6. 0.546
Number
up or down
nearest
hundred
Number
7. 371
10. 15.613
8. 6,121
11. 0.939
9. 82,345
12. 45.382
© Scott Foresman, Gr. 5
(16)
up or down
nearest tenth
nearest
up or down hundredth
Use with Chapter 1, Lesson 6.
Name _____________________________________________________________________________________________________
Rounding Whole Numbers and Decimals
H 1-6
Complete the cross-number puzzle. Place the decimal point in each answer
in a square of its own. The first one is done for you.
Across
Down
Round . . .
Round . . .
1. 25.863 to tenths
2. 968,799 to hundreds
4. 73.4135 to tenths
3. 3,486.376 to hundredths
7. 81,873 to tens
5. 34.999 to tenths
8. 46.111 to hundredths
6. 40.599 to hundredths
9. 6,407.556 to hundredths
9. 62,594 to tens
10. 50.089 to hundredths
10. 5,316 to tens
12. 93.47 to tenths
11. 9,349 to hundreds
13. 83,248 to hundreds
1
2
5
.
2
3
9
4
5
6
7
8
9
10
12
11
13
Test Prep Choose the correct letter for each answer.
14. Find 13 ! n if n " 12
15. Find n if 17 ! 5 " 5 ! n
A 25
C 1
F 5
H 85
B 13
D 156
G 12
J 17
© Scott Foresman, Gr. 5
(17)
Use with Chapter 1, Lesson 6.
Name _____________________________________________________________________________________________________
Variables and Tables
R 1-7
The same rule is used with each number in Column A, and the corresponding result
is given in Column B. To find the rule, follow these steps.
Step 1
Step 2
Look at the first pair of numbers.
Decide how they are related.
2!3=6
Check this method for the next pair of numbers.
3 ! 3 = 9, not 7
Go back to the first pair.
Find another way the numbers are related.
2+4=6
Check this for other pairs.
3+4=7
5+4=9
6 + 4 = 10
A
B
2
6
3
7
5
9
6
10
12
16
The relationship is the same for all pairs so the rule is add 4.
You can write this rule using a variable, n, to represent the numbers in Column A.
The rule is n + 4.
Find the rule for each table. Write the rule in words and using a variable. Let the variable
represent any number in Column A.
1.
A
B
8
2.
3.
4.
A
B
3
13
22
63
9
17
26
30
70
10
23
32
8
48
84
12
27
36
9
54
91
13
31
40
A
B
2
1
12
6
24
A
B
6
21
3
18
18
5
30
24
40
34
Write each rule using a variable.
5. Add 12 to a number.
© Scott Foresman, Gr. 5
(19)
6. Divide a number by 6.
7. Multiply a number by 7.
Use with Chapter 1, Lesson 7.
Name _____________________________________________________________________________________________________
Variables and Tables
H 1-7
Complete each table. Write the rule using words and using a variable. Let the variable
represent any number in column A.
1.
2.
B
0
24
13
0
37
B
0
1
3
4
B
1
4
3.
56
6
6
9
9
8
20
0
A
B
45
74
0
10
12
4.
A
A
A
83
72
95
84
A
B
17
16
A
B
24
15
13 143
12
2
43
34
15 165
24
4
56
16 176
48
8
70
17
96
5.
6.
88
79
21 231
192
91
82
23 253
384
64
Test Prep Choose the correct letter for each answer.
7. Write the rule using a variable.
Add 13 to a number.
8. Write the rule using words.
n & 12
A n + 13
C n - 13
F add 12
H subtract 12
B n # 13
D n & 13
G multiply by 12
J divide by 12
© Scott Foresman, Gr. 5
(20)
Use with Chapter 1, Lesson 7.
Name _____________________________________________________________________________________________________
Problem-Solving Application
R 1-8
Using Data from Tables and Graphs
Understand You need to find the
length of time it took the class to collect
25 pounds of recyclables.
Plan Use the graph and your knowledge
of number order.
Solve You know that 25 comes halfway
between 20 and 30. To find the time
needed to collect 25 pounds on the graph,
find the line between 20 and 30 on the
vertical scale. Follow the dotted line to the
right until it meets the heavy black line.
Then, follow the dotted line down from that
point to the number of weeks at the bottom.
The number of weeks is halfway between 2
and 3. The class collected 25 pounds of
recyclables in about 2!12! weeks.
Look Back The answer is reasonable
because the table shows that the class can
collect 20 pounds of recyclables in 2 weeks
and 30 pounds of recyclables in 3 weeks.
25 is halfway between 20 and 30 and
2!12! weeks is halfway between 2 weeks
and 3 weeks.
Pounds of Recyclables Collected
100
90
80
70
60
50
40
30
20
10
Number of Pounds
Marcy’s 5th grade class collected bottles and
cans for their school’s recycling center. They
made the graph at the right to show how many
pounds of recyclable bottles and cans they
collected. How long did it take them to collect
25 pounds of bottles and cans?
0
1 2 3 4 5 6 7 8 9 10
Number of Weeks
Number of
Pounds of
Recyclables
Number of
Weeks
10
1
20
2
30
3
40
4
50
5
60
6
70
7
80
8
90
9
100
10
Use the graph to solve the problems.
1.
About how long does it take the class to collect 75 pounds of recyclables?
2.
About how many pounds does the class collect in 3 1/2 days?
© Scott Foresman, Gr. 5
(22)
Use with Chapter 1, Lesson 8.
Name _____________________________________________________________________________________________________
Problem-Solving Application
H 1-8
Using Data from Tables and Graphs
Wesley plans to ride in a fundraising bike-a-thon this spring. He drew a graph to show how
far he could bike in eight hours. The graph and the table show Wesley’s biking rate. Use
them to answer the questions below.
Number of
Hours
30
2
60
4
90
8
120
Number of Miles
Number of
Miles
90
60
30
0
2
4
6
8
Number of Hours
1.
To get in shape for the race, Wesley biked from 10:00 to noon. How many miles
did he travel?
2.
About how long will it take Wesley to bike 50 miles?
3.
During a pre-race trial, Wesley’s team biked for one hour. About how many miles
did they travel?
4.
Wesley’s sponsors have pledged to donate $10 a mile. How much money will
Wesley raise in 6 hours?
5.
How long will Wesley need to bike to raise over $1,000?
© Scott Foresman, Gr. 5
(23)
Use with Chapter 1, Lesson 8.