Name
Understanding Decimals
R 2-1
A decimal is a number that uses a decimal point. Each digit in a
decimal number has a place and value. You can use a place-value
chart to determine a digit’s place and value.
2
6
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hu dth
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sa d
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decimals
hs
ones
8
4
The 8 is in the thousandths place. Its value is 8 thousandths, or 0.008.
The standard form of the number is 5.2684. The word form is five and
two thousand, six hundred eighty-four ten thousandths.
The expanded form is:
0.2 0.06 0.0004.
Give the place and value of the 9 in each number.
1. 2.195
2. 6.2394
3. 34.32629
Complete the table.
Standard Form
2.346
Expanded Form
2 and 346 thousandths
1 0.6 0.0009
5.
8
8
6. Number Sense Express 18
, and as decimal numbers.
0, 100
10,000
7. Writing in Math Explain how you know that 17 thousandths has
more than two places to the right of the decimal point.
18
Use with Lesson 2-1.
© Pearson Education, Inc. 6
4.
Short-Word Form
Name
Comparing and Ordering Decimals
R 2-2
Use a number line
Remember, as you move to the right on a number line, the numbers are
greater in value. As you move to the left, the numbers are lesser in value.
Compare 0.332 and 0.323.
0.332
0.323
0.320
0.330
0.340
lesser
greater
Since 0.332 is to the right of 0.323, 0.332 0.323.
Align the digits
Order 3.27, 4.86, 3.09, and 3.85 from least to greatest.
Order
ones.
Order
tenths.
3.
3.
3.
4.
3.
3.
3.
4.
• Start at the left and compare digits in the same place value.
• Order the digits by place value.
27
09
85
86
0
2
8
8
9
7
5
6
In order from least to greatest, the numbers are:
,
,
,
.
Use , , or to compare each pair of numbers.
1. 3.030
3. 1.39292
3.03
13.9232
2. 9.3226
4. 0.135
9.3262
0.0135
Order from least to greatest.
© Pearson Education, Inc. 6
5. 23.4 24.4 24.34
6. 16.03 16.30 16.003
7. 2.5021 2.00251 2.05021 2.00502
8. Writing in Math Explain why 37.75 is greater than 37.07.
Use with Lesson 2-2.
19
Name
Rounding Decimals
R 2-3
Round 0.168 to the nearest hundredth.
0.168
0.16 8
Find the rounding place.
Look at the digit to the
right of this place.
If the digit is 5 or greater, add
1 to the rounding digit. If the
digit is less than 5, leave the
rounding digit alone.
Drop the digits to the right
of the rounding digit.
Round 0.721 to the nearest hundredth.
85
The digit
is in the hundredths
place. The digit to the right is less than 5,
so leave the rounding digit alone.
0.17
So, 0.721 rounded to
the nearest hundredth is
.
So, 0.168 rounded to the nearest
hundredth is 0.17.
Round to the underlined place.
1. 71.247
2. 3.731
3. 6.189
4. 22.6233
5. 3.0156
6. 5.1079
7. 45.45151
8. 0.00675
9. 1.555
10. 437.821
11. 10.9711
12. 87.24627
14. Reasoning Does the number in the tenths place change
when you round 3.1678 to the nearest hundredth? Explain
your answer.
20
Use with Lesson 2-3.
© Pearson Education, Inc. 6
13. Number Sense A number rounds to 5.68. Write one possibility
for the number.
Name
Estimating with Decimals
R 2-4
You can use rounding and compatible numbers to estimate with decimals.
Jane bought a shirt for $29.99, a hat for $9.75, and a pair of socks
for $5.12. About how much did she spend?
Round each number to the nearest dollar, then add.
So, Jane spent about $45.00.
Estimate 78.12 3.88.
$29.99
$ 9.75
$ 5.12
$30.00
$10.00
$ 5.00
$45.00
Find compatible numbers.
78.12 is close to 80 and 3.88 is close to 4.
Four is easy to divide into 80.
80 4 20
So, 78.12 3.88 ≈ 20.
Estimate each answer.
1. 15.03 4.89
2. $18.33 $9.84
3. $11.85 $4.27
4. $9.66 $6.12
5. 3.89 7.0202
6. 4.03 11.0086
7. 23.95 9.828
8. 480.456 48.003
9. Writing in Math Why would it make sense to use compatible
numbers to estimate 43.56 4.912?
© Pearson Education, Inc. 6
10. Reasoning About how much would 11 cans
of beans cost? How did you get your answer?
Gene’s Groceries
Can of beans
Package of pita bread
Package of crescent rolls
Large yogurt
Salmon fillet
$0.89
$3.75
$2.99
$1.81
$5.87
11. Wendi needs to buy 5 packages of
pita bread and 3 packages of crescent
rolls. About how much will she spend?
Use with Lesson 2-4.
21
Name
Adding and Subtracting
Whole Numbers and Decimals
R 2-5
Find 2.3 0.09 41.6.
Estimate: 2 0 42 44
2.30
0.09
41.60
43.99
Write the numbers, lining up the decimal
points. Annex zeros so all numbers have
the same number of decimal places.
Add the numbers. Regroup if necessary.
Write the decimal point in your answer.
Since 43.99 is close to 44, the answer is reasonable.
Find 18.5 7.82.
Estimate: 19 8 11
7 4
Write the numbers, lining up the decimal
points. Annex zeros so all numbers have
the same number of decimal places.
Subtract the numbers. Regroup if necessary.
Write the decimal point in your answer.
18.50
7.82
10.68
Since 10.68 is close to 11, the answer is reasonable.
Find each sum or difference.
1. 45.6 26.3
2. 84.84 22.7
3. 77 3.09
4. 14.25 5.17
5. 23.64 8.73
6. 29 0.45
8. 5,712.11 921.79 5.35
9. Estimation Estimate the sum of 3.7 and 9.8.
10. Find the total distance all three
cars have traveled.
22
Use with Lesson 2-5.
Mr. Cortez
13052.64
Ms. Brown
6520.10
Gerrie
920.70
© Pearson Education, Inc. 6
7. 17.08 14.04 2.30
Name
Multiplying Whole Numbers
and Decimals
Find 12.7 2.4.
R 2-6
1
12
Estimate: 13 2 26
Multiply as you would with whole numbers.
Count the total number of decimal places
in both factors. Start at the right of the
product. Move to the left the total number
of decimal places in both factors. Sometimes
you have to annex zeros to the left of the
product to place the decimal point correctly.
12.7
2.4
1 508
2540
30.48
one decimal place
one decimal place
two decimal places
from the right
Place the decimal point in each product.
1. 1.2 3.6 432
2. 5.5 3.77 20735
3. 4.4 2.333 102652
4. 4 5.2
5. 2.7 2.6
6. 14.8 3.7 10
7. 4.6 0.3 100
8. 0.2 0.61
9. 17 0.087
Find each product.
© Pearson Education, Inc. 6
10. 0.53 12.8
11. 8 0.06
12. Number Sense Two factors are multiplied and their product is
34.44. One factor is a whole number. How many decimal places
are in the other factor?
13. Writing in Math How many decimal places will be in the
product 4.5 0.007? Explain.
Use with Lesson 2-6.
23
Name
Dividing by a Whole Number
R 2-7
Dividing a decimal by a whole number is similar to dividing whole
numbers by whole numbers.
Find 196 32.
Estimate: 210 30 7
Step 1 Divide. Put the decimal
point in dividend and quotient.
6.
32 196.
192
4
Step 2 Annex a zero. Divide.
Subtract then bring down.
Step 3 Repeat until there is no
remainder.
6.1
32 196.0
192
40
3 2
8
6.125
32 196.000
192
40
3 2
80
64
160
160
0
Since 6.125 is close to 7, the
answer is reasonable.
1. 92
0
.7
2. 63
1
.2
3. 72
2
.6
1
4. 119
3
.5
5. 124
.5
6. 84
0
1
.2
7. Marcus purchased a 12 lb bag of trail mix. He paid $10.80. Find
the price per pound.
8. Writing in Math Destiny said that 0.6 2 0.3. Is she correct?
Explain why or why not.
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Use with Lesson 2-7.
© Pearson Education, Inc. 6
Find each quotient. Round to nearest hundredth if necessary.
Name
PROBLEM-SOLVING SKILL
R 2-8
Interpreting Remainders
Author Donna is writing a 108-page book. If she plans to write 16
pages per day, how many days will it take her to write the book?
Divide to find the answer.
Estimate: 105 15 7
6 R12
16 108
96
remainder
12
Sometimes quotients include a remainder. The
remainder represents 12 extra pages that need to
be written. Donna will need another day to write
the rest of the pages.
Since 6 R12 is close to 7, your answer is reasonable.
Donna will need 7 days to write her book.
Sports Cards James collects sports cards. He stores them in plastic
carriers. Each carrier holds 9 cards.
1. James has 138 cards. How many carriers will he
need to store all his cards?
2. What does the remainder or decimal part of your answer represent?
3. How many cards are left over?
4. How many carriers will be completely filled?
© Pearson Education, Inc. 6
Moving Day Mara is moving her CD collection. She has
to bring her 235 CDs from her old room to her new room upstairs.
5. Mara can only carry 20 CDs at a time. How many
trips will she need to take?
6. What does the remainder or decimal part of your answer represent?
7. How many CDs will she carry on her last trip?
Use with Lesson 2-8.
25
Name
Dividing by a Decimal
R 2-9
Find 4.728 0.6.
Estimate: 48 6 8
Count the number of
decimal places in the
divisor.
Step 1 Move the
decimal point to make
the divisor a whole
number.
.6 4.728
one
decimal
place
6. 4.728
decimal point
moved to make
.6 become 6.
Step 2 Move the
decimal point in the
dividend the same
number of spaces
(4.728 10 47.28).
Then write the decimal
point in the quotient at
the same place.
.
6. 47.28
moved
one
decimal
place
moved
one
decimal
place
Step 3 Divide the same
way you do with whole
numbers.
7.88
6 47.28
42
52
48
48
48
0
1. 0.71
.7
5
2. 0.83
.6
2
4
3. 1.10
.6
3
9
1
4. 2.21
4
3
5. 0.090
.0
5
6
9
7
6. 0.151
.1
4
6
7. Writing in Math Wendy divided 147 by 0.7. Jan divided 1,470 by 7.
Should they both get the same answer? Explain.
26
Use with Lesson 2-9.
© Pearson Education, Inc. 6
Find each quotient.
Name
Multiplying and Dividing by
Powers of Ten
R 2-10
Multiplying a number by a positive
power of ten
Multiplying a number by a negative
power of ten
Find 3.15 103.
Find 7.34 103. Remember 103 0.001. So it is the same as 7.34 0.001.
Move the decimal point the same
number of places to the right as the
exponent. Annex zeros if you need to.
3.150
Move the decimal point the same number
of places to the left as the exponent. Add
zeros if you need to.
So, 7.34 103 0.00734.
So, 3.15 103 3,150.
Dividing a number by a positive
power of ten
Dividing a number by a negative
power of ten
Find 42.6 103.
Find 24 104. Remember 104 0.0001. So it is the same as 24 ÷ 0.0001.
Move the decimal point the same
number of places to the left as the
exponent. Annex zeros if you need to.
042.6
Move the decimal point the same number
of places to the right as the exponent.
Add zeros if you need to.
So, 24 104 240,000.
So, 42.6 103 0.0426.
© Pearson Education, Inc. 6
Find each product or quotient.
1. 1,357 102 2. 0.00471 105 3. 25.346 103 4. 52.5 102 5. 139.3 106 6. 47.1303 104 7. Number Sense What happens to the dividend when you divide
it by a negative exponent?
8. In 2000, the total value of all new cars that Americans bought
was $274.5 109. Write this number in standard form.
Use with Lesson 2-10.
27