Table of Contents
All About Decimals
Table of Contents
Introduction to the Teacher ......................................................................................................... 1
Common Core State Standards Matrix ...................................................................................... 2
Meaning of Decimals
Reading and Writing Decimals in Tenths ............................................................................ 3
Reading and Writing Decimals in Hundredths .................................................................... 5
Reading and Writing Decimals in Thousandths .................................................................. 7
Place Value Through Thousandths ..................................................................................... 9
Comparing Decimals ........................................................................................................ 11
Ordering Decimals ............................................................................................................ 13
Rounding Decimals........................................................................................................... 15
Unit Assessment ............................................................................................................... 17
Adding and Subtracting Decimals
Adding Decimals ............................................................................................................... 19
Subtracting Decimals ........................................................................................................ 21
Unit Assessment ............................................................................................................... 23
Multiplying Decimals
Counting Decimal Places.................................................................................................. 25
Multiplying a Decimal by a Whole Number ....................................................................... 27
Multiplying a Decimal by a Decimal .................................................................................. 29
Multiplying Decimals—Zero in the Product ....................................................................... 31
Multiplying Decimals by 10, 100, or 1,000 ........................................................................ 33
Unit Assessment ............................................................................................................... 35
Dividing Decimals
Dividing a Decimal by a Whole Number ........................................................................... 37
Dividing by a Decimal ....................................................................................................... 39
Dividing Decimals—Rounding Quotients .......................................................................... 41
Dividing Decimals by 10, 100, or 1,000 ............................................................................ 43
Converting Decimals to Fractions ..................................................................................... 45
Converting Fractions to Decimal ....................................................................................... 47
Converting Percents to Decimals...................................................................................... 49
Unit Assessment ............................................................................................................... 51
Learning Stations Center-Based Activities ............................................................................. 53
Daily Math Review ..................................................................................................................... 58
Glossary of Terms ..................................................................................................................... 60
Answer Keys .............................................................................................................................. 61
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Reading and Writing Decimals in Tenths
All About Decimals
Lesson Introduction: Reading and Writing Decimals in Tenths
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.8.NS.A.1
Objective
• Identify parts of a decimal.
• Read and write decimals to tenths.
• Read and write decimals in standard, word,
and expanded form.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, decomposition, expanded form, standard form, tenths, word form
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided into
ten equal parts is divided into tenths. A decimal point is a dot placed after the figure representing
units in a decimal fraction.
Meaning of Decimals
Examples
0.1
2.4
The decimal point is read
as and in numbers greater than 1.0. The decimal
for the example to the left
would be read as two and
four-tenths
If a whole is divided
into 10 equal parts,
each part is 1 tenth.
Place Value
Examples
Ones
0
2
Decimal Point
.
.
Tenths
1
4
Writing Decimals
A decimal can be written in standard form, word form, or expanded form. A decimal written
in standard form is written as a number. When a decimal is written in standard form, a decimal
point separates the whole number part of the decimal from the part that is less than 1. Read
the number from left to right. Read as a whole number, followed by the last digit’s place value. A
decimal written in word form is written as words. Insert a hyphen between the numerator and the
denominator, unless the numerator or denominator is already a hyphenated number. A decimal
written in expanded form is a way to break the number down (decomposition) into several more
easily managed numbers.
Examples
Standard Form
3.1
Word Form
three and one-tenth
Problems to Try
a. Write the standard form of four-tenths.
Answer: 0.4
Expanded Form
3 + 0.1
b. Write the word form of 5.9.
Answer: five and nine-tenths
Real-World Connection
You use decimals every time you use money. The amount of money $2.55 means you have
two whole dollars and 55 equal parts of another dollar.
404213-EB ©Mark Twain Media, Inc., Publishers
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Reading and Writing Decimals in Tenths
All About Decimals
Name:
Date:
Practice: Reading and Writing Decimals in Tenths
Directions: Write each decimal represented by the pictures.
1.
2.
3.
Directions: Write the following decimals in the table.
Ones
Decimal Point
4. five and three-tenths
5. seven-tenths
6. four and eight-tenths
7. What is the standard form of one and four-tenths?
8. What is the standard form of nine and two-tenths?
9. What is the word form of 0.4?
10. Write the expanded form of 5.9.
Apply
11. Kathy walked eight-tenths of a mile. Write the decimal.
12. Alex and Dawn hiked 5.5 miles on the park trail. Write the decimal in
words.
404213-EB ©Mark Twain Media, Inc., Publishers
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Tenths
Reading and Writing Decimals in Hundredths
All About Decimals
Lesson Introduction: Reading and Writing Decimals in
Hundredths
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.8.NS.A.1
Objective
• Identify parts of a decimal.
• Read and write decimals to hundredths.
• Read and write decimals in standard, word,
and expanded form.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, decomposition, expanded form, hundredths, standard form, word form
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided
into one hundred equal parts is divided into hundredths. A decimal point is a dot placed after the
figure representing units in a decimal fraction.
Meaning of Decimals
Examples
0.01
If a whole is
divided into
100 equal
parts, each
part is
1 hundredth.
The decimal point is read
as and in numbers greater
than 1.0. The decimal for
the example to the left
would be read as two and
fifty-three hundredths.
2.53
Place Value
Examples
Ones
0
2
Decimal Point
.
.
Tenths
0
5
Hundredths
1
3
Writing Decimals
A decimal can be written in standard form, word form, or expanded form. A decimal written
in standard form is written as a number. When a decimal is written in standard form, a decimal
point separates the whole number part of the decimal from the part that is less than 1. Read
the number from left to right. Read as a whole number, followed by the last digit’s place value. A
decimal written in word form is written as words. A decimal written in expanded form is a way to
break the number down (decomposition) into several more easily managed numbers.
Examples
Standard Form
4.32
Word Form
Four and thirty-two hundredths
Problems to Try
a. Write the word form of 6.61.
Answer: six and sixty-one hundredths
Expanded Form
4 + 0.3 + 0.02
b.
1 tenth =
Answer: 10
hundredths
Real-World Connection
You use decimals every time you use money. There are 100 pennies in a dollar. One penny
is one-hundredth of a dollar or $0.01.
404213-EB ©Mark Twain Media, Inc., Publishers
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Reading and Writing Decimals in Hundredths
All About Decimals
Name:
Date:
Practice: Reading and Writing Decimals in Hundredths
Directions: Write each decimal represented by the pictures.
1.
2.
3.
Directions: Write the following decimals in the table.
4.
forty-four hundredths
Tens
Ones
5. twenty-five and eighteen-hundredths
Decimal Point
Tenths
6. four-hundredths
Hundredths
7. What is the standard form of two and eight-hundredths?
8. What is the standard form of thirteen and twenty-six hundredths?
9. What is the word form of 3.04?
10. Write the expanded form of 82.19.
Apply
11. A candy bar cost 88¢. Write the decimal.
12. Jerry spent $15.97 at the convenience store. Write the decimal in words.
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