Learn on PengiEureka Math, Grade 4Chapter 30: Tenths and Hundredths

Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.

In this Grade 4 Eureka Math lesson from the Tenths and Hundredths chapter, students use fraction equivalence to express decimal numbers in different units on the place value chart, converting between ones, tenths, and hundredths. Using area models and place value disks, students explore how a number like 2.4 can be expressed as 24 tenths or 240 hundredths, reinforcing that 0.4 equals 0.40. Students also practice writing decimals and mixed numbers in expanded decimal and expanded fraction form.

Section 1

Conceptual Model: Relating Adjacent Place Value Units

Property

Each place value unit is 10 times greater than the unit to its immediate right.
This creates a multiplicative relationship where one of a larger unit can be decomposed into ten of the next smaller unit.

1 \text{ one} = 10 \text{ tenths}

1 \text{ tenth} = 10 \text{ hundredths}

1 \text{ one} = 100 \text{ hundredths}

Examples

Section 2

Decomposing Decimals into Smaller Units

Property

To express a decimal number as a total number of a smaller unit, decompose each larger place value into the target unit and sum the results.

Total tenths = $(ones \times 10) + tenths$
Total hundredths = $(ones \times 100) + (tenths \times 10) + hundredths$

Examples

Section 3

Representing Decimals in Equivalent Fraction Forms

Property

A decimal number can be expressed in various equivalent forms, such as a mixed number or an improper fraction, by relating it to tenths and hundredths. Adding a trailing zero to a decimal renames it in smaller units without changing its value.

2.4 = 2 \frac{4}{10} = \frac{24}{10}

2.4 = 2.40 = 2 \frac{40}{100} = \frac{240}{100}

Examples

Book overview

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Chapter 30: Tenths and Hundredths

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Lesson 1
Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.
Learn Practice
Lesson 2
Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.
Learn Practice
Lesson 3
Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.
Learn Practice
Lesson 4
Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.
Learn Practice
Lesson 5Current
Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.
Learn Practice

Lesson overview

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Section 1

Conceptual Model: Relating Adjacent Place Value Units

Property

1 \text{ one} = 10 \text{ tenths}

1 \text{ tenth} = 10 \text{ hundredths}

1 \text{ one} = 100 \text{ hundredths}

Examples

Section 2

Decomposing Decimals into Smaller Units

Property

To express a decimal number as a total number of a smaller unit, decompose each larger place value into the target unit and sum the results.

Total tenths = $(ones \times 10) + tenths$
Total hundredths = $(ones \times 100) + (tenths \times 10) + hundredths$

Examples

Section 3

Representing Decimals in Equivalent Fraction Forms

Property

2.4 = 2 \frac{4}{10} = \frac{24}{10}

2.4 = 2.40 = 2 \frac{40}{100} = \frac{240}{100}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 30: Tenths and Hundredths

Back to Eureka Math, Grade 4

Lesson 1
Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.
Learn Practice
Lesson 2
Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.
Learn Practice
Lesson 3
Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.
Learn Practice
Lesson 4
Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.
Learn Practice
Lesson 5Current
Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Conceptual Model: Relating Adjacent Place Value Units

Property

1 \text{ one} = 10 \text{ tenths}

1 \text{ tenth} = 10 \text{ hundredths}

1 \text{ one} = 100 \text{ hundredths}

Examples

Section 2

Decomposing Decimals into Smaller Units

Property

To express a decimal number as a total number of a smaller unit, decompose each larger place value into the target unit and sum the results.

Total tenths = $(ones \times 10) + tenths$
Total hundredths = $(ones \times 100) + (tenths \times 10) + hundredths$

Examples

Section 3

Representing Decimals in Equivalent Fraction Forms

Property

2.4 = 2 \frac{4}{10} = \frac{24}{10}

2.4 = 2.40 = 2 \frac{40}{100} = \frac{240}{100}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 30: Tenths and Hundredths

Back to Eureka Math, Grade 4

Lesson 1
Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.
Learn Practice
Lesson 2
Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.
Learn Practice
Lesson 3
Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.
Learn Practice
Lesson 4
Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.
Learn Practice
Lesson 5Current
Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.
Learn Practice

Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.

Property

Examples

Property

Examples

Property

Examples

Chapter 30: Tenths and Hundredths

Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.

Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.

Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.

Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.

Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.

Lesson overview

Property

Examples

Property

Examples

Property

Examples

Chapter 30: Tenths and Hundredths

Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.

Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.

Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.

Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.

Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.

Lesson 1: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths.

Lesson 2: Model the equivalence of tenths and hundredths using the area model and place value disks.

Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.

Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.

Lesson 5: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units.