Learn on PengiEureka Math, Grade 4Chapter 29: Exploration of Tenths

Lesson 3: Represent mixed numbers with units of tens, ones, and tenths with place value disks, on the number line, and in expanded form.

In this Grade 4 Eureka Math lesson from Chapter 29, students learn to represent mixed numbers containing units of tens, ones, and tenths using three models: place value disks, the number line, and expanded form. Students practice converting between improper fractions, mixed numbers, and decimals, and explore how 10 tenths can be renamed as one whole. The lesson builds foundational understanding of decimal place value and prepares students for decimal fraction addition.

Section 1

Representing Mixed Numbers with Tenths on a Number Line

Property

To plot a mixed number on a number line, first locate the whole number part. The interval between each whole number is partitioned into 10 equal segments, each representing one-tenth (110\frac{1}{10} or 0.10.1). From the whole number, count forward by the number of tenths to find the exact location.

Examples

Section 2

Writing Numbers in Expanded Form

Property

A number with tens, ones, and tenths can be written in expanded form by multiplying each digit by its place value. This can be expressed using fractions or decimals.
Fraction Form:

(a×10)+(b×1)+(c×110)(a \times 10) + (b \times 1) + (c \times \frac{1}{10})

Decimal Form:
(a×10)+(b×1)+(c×0.1)(a \times 10) + (b \times 1) + (c \times 0.1)

Examples

Section 3

Making the Next Whole

Property

To find the value needed to get from a decimal to the next whole number, find the amount that must be added to the tenths to make one whole (1010 tenths).

current_decimal+value_needed=next_whole_numbercurrent\_decimal + value\_needed = next\_whole\_number

Examples

Book overview

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Chapter 29: Exploration of Tenths

  1. Lesson 1

    Lesson 1: Use metric measurement to model the decomposition of one whole into tenths.

    LearnPractice
  2. Lesson 2

    Lesson 2: Use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers.

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Represent mixed numbers with units of tens, ones, and tenths with place value disks, on the number line, and in expanded form.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Representing Mixed Numbers with Tenths on a Number Line

Property

To plot a mixed number on a number line, first locate the whole number part. The interval between each whole number is partitioned into 10 equal segments, each representing one-tenth (110\frac{1}{10} or 0.10.1). From the whole number, count forward by the number of tenths to find the exact location.

Examples

Section 2

Writing Numbers in Expanded Form

Property

A number with tens, ones, and tenths can be written in expanded form by multiplying each digit by its place value. This can be expressed using fractions or decimals.
Fraction Form:

(a×10)+(b×1)+(c×110)(a \times 10) + (b \times 1) + (c \times \frac{1}{10})

Decimal Form:
(a×10)+(b×1)+(c×0.1)(a \times 10) + (b \times 1) + (c \times 0.1)

Examples

Section 3

Making the Next Whole

Property

To find the value needed to get from a decimal to the next whole number, find the amount that must be added to the tenths to make one whole (1010 tenths).

current_decimal+value_needed=next_whole_numbercurrent\_decimal + value\_needed = next\_whole\_number

Examples

Book overview

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

Continue this chapter

Chapter 29: Exploration of Tenths

  1. Lesson 1

    Lesson 1: Use metric measurement to model the decomposition of one whole into tenths.

    LearnPractice
  2. Lesson 2

    Lesson 2: Use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers.

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Represent mixed numbers with units of tens, ones, and tenths with place value disks, on the number line, and in expanded form.

    LearnPractice