Understanding Decimals

Name
Understanding Decimals
P 2-1
Give the place and value of the 3 in each number.
1. 56.389
2. 9.6431
3. 0.72536
Complete the table.
Standard Form
Short-Word Form
Expanded Form
2 and 3 hundredths
4.
70 8 0.4 0.06
5.
44
4
44
6. Number Sense Express 14
as decimal numbers.
0, 10
0 , and 1,000
Write the total number of points for each event in expanded form.
7. team
Event
Winning Points
Team
154.608
All-around
8. all-around
Uneven bars
38.642
9.862
9. uneven bars
10. Which shows the short-word form for 16.011?
A. 16 and 11 thousandths
B. 16 and 11 hundredths
C. 16 and 11 tenths
D. 16 0.011
11. Writing in Math Explain how to determine the place and value
of a number.
18
Use with Lesson 2-1.
© Pearson Education, Inc. 6
Test Prep
Name
P 2-2
Comparing and Ordering Decimals
Use , , or to compare each pair of numbers.
1. 656.07
3. 0.01
656.23
0.10
2. 73.42
72.56
4. 7.999
7.998
Order from least to greatest.
5. 639.087, 639.078, 638.088
6. 0.0909, 0.0989, 0.0999
7. 19.235, 19.23, 19.240, 19.2353
8. Order the lung volumes from least
to greatest.
Animal (adult)
9. Which animal has a lung volume that
is greater than a cow’s?
Lung Volume
(in quarts)
Cat
0.328
Cow
10.565
Mouse
0.001
Whale
105.65
10. Which two animals have the closest
lung volume?
© Pearson Education, Inc. 6
Test Prep
11. Which decimal is greater than 3.33 but less than 3.34?
A. 2.3349
B. 3.305
C. 3.329
D. 3.336
12. Writing in Math Explain how to find a number that is between
4.9 and 4.95.
Use with Lesson 2-2.
19
Name
Rounding Decimals
P 2-3
Round to the underlined place.
1. 0.0043
2. 84.638
3. 2.984
4. 217.4
5. 0.0017
6. 2.709
7. 371.902
8. 45.99
9. Number Sense A number rounds to 6.78. List three possibilities
for the number.
Departure City
Destination City
Fare
Portland
San Diego
$208.75
San Diego
Denver
$310.45
Denver
Portland
$296.97
Round each of the round-trip fares to the nearest one dollar.
Then round to the nearest ten cents.
10. Portland to San Diego
11. San Diego to Denver
12. Denver to Portland
Test Prep
A. 6.7688
B. 6.7669
C. 6.7659
14. Writing in Math Explain how 1.1, 1.06, and 1.059 can all be
rounded forms of 1.0592.
20
Use with Lesson 2-3.
D. 6.7654
© Pearson Education, Inc. 6
13. Which number can round to 6.766?
Name
Estimating with Decimals
P 2-4
Estimate each answer.
1. $36.17 $42.89
2. 25.9 12.8
3. 78.11 5.7
4. 132.36 48.31
5. $421.90 $20.10
6. 16.48 3.2
7. 94.951 67.632
8. $37.55 $83.69
9. Number Sense Is 2 or 4 a better estimate for the quotient
47.8 11.6? Explain.
10. Victoria has $10 to spend on her new puppy.
Name 3 different items she can buy.
11. Joe has $5 to spend on his dog, Frisky. Can he
buy the food dish and a brush? Why or why not?
Pet Supplies
Food dish
Water bowl
Leash
Squeaky toy
Rope toy
Brush
$2.69
$2.39
$5.29
$1.32
$2.45
$4.00
12. Mental Math Estimate the total for all the items.
© Pearson Education, Inc. 6
Test Prep
13. Which is the most reasonable estimate for the total of
$22.16 $57.89 $46.41?
A. $110
B. $130
C. $180
D. $250
14. Writing in Math You want to buy supplies for a school project.
Explain why you would want an estimate to be greater than the
exact answer.
Use with Lesson 2-4.
21
Name
Adding and Subtracting Whole
Numbers and Decimals
P 2-5
Find each sum or difference.
1. 22 0.99 2. 9.8347 1.26 3. 5.011 1.23 23.7629 4. 101.21 45.6 5. 0.03 1.85 6. $67.85 $97.12 7. Number Sense Use each of the digits 0, 1, 2, 3, 4, and 5 exactly
once to write a decimal subtraction problem. The difference must
be the same as one of the decimals in the problem.
8. Find the difference in price
between the cost of 1 tube
of glue and 1 roll of tape.
9. Find the cost of 2 packs of
markers.
Craft Supplies
Poster board
$1.29/sheet
Markers
$4.50/pack
Tape
$1.99/roll
Construction paper
$3.79/pack
Glue
$2.39/tube
Test Prep
11. Which is the difference of 8,246.4 57.73?
A. 8,067.03
B. 8,144.06
C. 8,187.07
D. 8,188.67
12. Writing in Math Is 9.008 the correct answer for 9.009 0.01?
If not, tell why and provide the correct answer.
22
Use with Lesson 2-5.
© Pearson Education, Inc. 6
10. How much more do 2 packs of markers cost
than 4 sheets of poster board?
Name
Multiplying Whole Numbers
and Decimals
P 2-6
Place the decimal point in each product.
1. 3 6.892 20676
2. 0.3 4.57 1371
Find each product.
3. 14.3 2.1 8.9 4. 0.45 0.01 5. 67.1 0.3 0.4 6. 582.1 4.2 7. Reasoning Show how to find the product of 16.2 4 using addition.
8. Which activity is 6 times faster
than the fastest rowing speed?
10. How fast would 1.5 times the
fastest rowing speed be?
100.9
85.38
36.4
14.23
5
F
sw ast
im es
m t
in
g
Fa
st
ru es
nn t
in
g
Fa
st
ro est
w
in
g
Fa
st
es
lu t
ge
Fa
st
th est
ba row
se n
ba
ll
mph
9. The fastest speed a table tennis
ball has been hit is 21.12 times
faster than the speed for the
fastest swimmer. What is the
speed for the table tennis ball?
Fastest Sporting Speeds
110
100
90
80
70
60
50
40
30
20
10
0
Human Activity
© Pearson Education, Inc. 6
Test Prep
11. Which is the product of 241.82 3.8?
A. 91.8916
B. 918.916
C. 9,189.16
D. 91,891.6
12. Writing in Math Explain why multiplying 37.4 0.01 gives a
product that is less than 37.4.
Use with Lesson 2-6.
23
Name
Dividing by a Whole Number
P 2-7
Find each quotient. Round to the nearest hundredth if necessary.
1. 77 4 2. 3.21 6 3. 14 80 4. $1.13 22 5. 130 10,000 6. 8.6 86 7. 231 11 8. 961.23 13 9. Number Sense How can you tell if 54.6 3 is greater than or
less than 54.6 30?
For 10 and 11, write the price per ounce of each type of nut butter to
the nearest cent.
10. peanut butter
Nut Butter
11. almond butter
Price per Container
Peanut
12 oz for $1.11
Cashew
11 oz for $3.30
Almond
16 oz for $2.24
12. Which type of nut butter is the most
expensive per ounce?
Test Prep
13. Find the quotient of 60.82 17. Round to the nearest hundredth.
B. 3.58
C. 3.59
14. Writing in Math Explain how you determined the price per
ounce of a 12 oz jar of peanut butter in Exercise 10.
24
Use with Lesson 2-7.
D. 3.6
© Pearson Education, Inc. 6
A. 3.577
Name
PROBLEM-SOLVING SKILL
P 2-8
Interpreting Remainders
Igneous Quarry Company needs to deliver 284 tons of granite to a
site that is 1,080 mi away from the company.
1. If each truck can carry a maximum load of 10 tons, how many
full trucks will be needed?
2. How many tons of granite will need to be carried by an extra truck?
3. If a truck driver drives 600 mi per day, how many days will it take
to drive 2,080 mi?
4. What does the remainder represent?
5. If the company charged $8,050 for the entire job, how much did
it charge per ton for delivery?
© Pearson Education, Inc. 6
6. What does the remainder represent and how did you adjust your
answer to allow for this?
7. If each truck gets 7 mi to the gallon, how many gallons
of gas will be needed for the 1,080 mi? (Round to the
nearest hundredth.)
8. Each truck holds 100 gal of gas. If the drivers start with a full
tank of fuel, how many times will they need to refuel?
Use with Lesson 2-8.
25
Name
Dividing by a Decimal
P 2-9
Find each quotient.
1. 8.4 0.3 2. 66.15 0.63 3. 10.5 1.5 4. 86 0.4 5. 72.8 1.4 6. 14.36 0.4 7. 2.87 0.01 8. 78.32 0.22 9. Reasoning Why would multiplying both the dividend and the
divisor by 10 sometimes make a problem easier to solve?
For each item, find
how many times greater
the 2002 cost is than
the 1960 cost. Round
your answer to the
nearest hundredth.
10. movie admission
Item
1960 Cost
2002 Cost
Movie admission
$0.75
$8.50
Regular popcorn
$0.25
$3.25
Regular drink
$0.35
$2.75
11. regular popcorn
12. regular drink
13. Which item has increased the greatest amount
of times from its original cost?
Test Prep
A. 156
B. 156.6
C. 156.61
15. Writing in Math Lynn and Randi got different
quotients when they divided 3.60 by 0.12.
Whose work is correct? Explain why.
26
Use with Lesson 2-9.
D. 156.63
Lynn
0.30
1 2) 3 . 6 0
Randi
30.0
1 2) 3 6 0 .
© Pearson Education, Inc. 6
14. Divide. Round to the nearest hundredth. 250.6 1.6
Name
Multiplying and Dividing by
Powers of Ten
P 2-10
Find each product or quotient.
1. 72.1 103 2. 450 10–4 3. 3.103 103 4. 167.4 10–2 5. 0.012 10–2 6. 0.012 102 7. 0.301 10–3 8. 8.235 104 9. Reasoning Explain in your own words why 104 is greater than 10–4.
10. Number Sense Write 10, 100, and 1,000 as powers of ten. Do
the same for 0.1, 0.01, and 0.001.
11. Write the weight of an ant in
standard form.
12. Write the weight of an elephant
in standard form.
Weight (in pounds)
Ant
2 105
Hummingbird
2 102
16 103
Elephant
© Pearson Education, Inc. 6
13. Write the weight of a hummingbird in standard form.
Test Prep
14. Which is the quotient of 10.06 ÷ 104?
A. 0.001006
B. 0.01006
C. 1,006
D. 100,600
15. Writing in Math Explain how you would write one billion as a
power of ten.
Use with Lesson 2-10.
27