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

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

In this Grade 4 Eureka Math lesson from Chapter 30, students learn to model the equivalence of tenths and hundredths using area models and place value disks, exploring how 10 hundredths equals 1 tenth. Through fluency practice and hands-on activities, students convert between fraction and decimal forms, such as recognizing that 1/10 and 10/100 represent the same value. This lesson builds foundational decimal place value understanding essential for comparing and computing with decimals.

Section 1

Numerical Equivalence of Tenths and Hundredths

Property

To create an equivalent fraction for tenths and hundredths, multiply or divide both the numerator and the denominator by 10.

a10=a×1010×10andb100=b÷10100÷10\frac{a}{10} = \frac{a \times 10}{10 \times 10} \quad \text{and} \quad \frac{b}{100} = \frac{b \div 10}{100 \div 10}

Examples

Section 2

Translating Between Decimal Representations

Property

A decimal value can be represented in multiple equivalent forms, which can be decomposed to show the value of each digit.

34100=0.34=3 tenths 4 hundredths=0.3+0.04 \frac{34}{100} = 0.34 = \text{3 tenths 4 hundredths} = 0.3 + 0.04

Examples

Book overview

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Chapter 30: Tenths and Hundredths

  1. Lesson 1

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

    LearnPractice
  2. Lesson 2Current

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

    LearnPractice
  3. 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.

    LearnPractice
  4. 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.

    LearnPractice
  5. Lesson 5

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

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Numerical Equivalence of Tenths and Hundredths

Property

To create an equivalent fraction for tenths and hundredths, multiply or divide both the numerator and the denominator by 10.

a10=a×1010×10andb100=b÷10100÷10\frac{a}{10} = \frac{a \times 10}{10 \times 10} \quad \text{and} \quad \frac{b}{100} = \frac{b \div 10}{100 \div 10}

Examples

Section 2

Translating Between Decimal Representations

Property

A decimal value can be represented in multiple equivalent forms, which can be decomposed to show the value of each digit.

34100=0.34=3 tenths 4 hundredths=0.3+0.04 \frac{34}{100} = 0.34 = \text{3 tenths 4 hundredths} = 0.3 + 0.04

Examples

Book overview

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

Continue this chapter

Chapter 30: Tenths and Hundredths

  1. Lesson 1

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

    LearnPractice
  2. Lesson 2Current

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

    LearnPractice
  3. 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.

    LearnPractice
  4. 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.

    LearnPractice
  5. Lesson 5

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

    LearnPractice