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

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

In this Grade 4 Eureka Math lesson from Chapter 29, students learn to decompose one whole into tenths using metric measurement, representing tenths in unit form, fraction form (1/10), and decimal form (0.1). Using hands-on tools like bags of rice measured in kilograms and meter strips, students build tape diagrams and number lines to connect the fraction and decimal notation for tenths. The lesson introduces the decimal point and establishes that one tenth, 1/10, and 0.1 are equivalent representations of the same value.

Section 1

Applying Tenths to Metric Units

Property

A tenth of a specific unit of measure is represented by writing the unit's abbreviation after the fraction or decimal. For any unit:

1 tenth of a unit=110 unit=0.1 unit1 \text{ tenth of a unit} = \frac{1}{10} \text{ unit} = 0.1 \text{ unit}

Examples

Section 2

Equivalence of Fractions and Decimals (Tenths)

Property

A fraction with a denominator of 10 is equivalent to a decimal in the tenths place. The numerator of the fraction becomes the digit to the right of the decimal point.

n10=0.n\frac{n}{10} = 0.n

Examples

  • 210=0.2\frac{2}{10} = 0.2
  • 510=0.5\frac{5}{10} = 0.5
  • 910=0.9\frac{9}{10} = 0.9

Explanation

A decimal number is another way to write a fraction. When a whole is divided into 10 equal parts, each part can be written as the fraction 110\frac{1}{10} or the decimal 0.10.1. The first place to the right of the decimal point is the tenths place, representing parts out of ten. Therefore, the fraction form and decimal form for tenths are equivalent and interchangeable.

Section 3

Composing One Whole with Tenths

Property

One whole is equivalent to 10 tenths. Pairs of tenths can be added together to compose one whole, which is written as 1.01.0 or 1010\frac{10}{10}.

0.3+0.7=1.00.3 + 0.7 = 1.0
310+710=1010=1\frac{3}{10} + \frac{7}{10} = \frac{10}{10} = 1

Examples

Book overview

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Chapter 29: Exploration of Tenths

  1. Lesson 1Current

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

  2. Lesson 2

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

  3. Lesson 3

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

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Applying Tenths to Metric Units

Property

A tenth of a specific unit of measure is represented by writing the unit's abbreviation after the fraction or decimal. For any unit:

1 tenth of a unit=110 unit=0.1 unit1 \text{ tenth of a unit} = \frac{1}{10} \text{ unit} = 0.1 \text{ unit}

Examples

Section 2

Equivalence of Fractions and Decimals (Tenths)

Property

A fraction with a denominator of 10 is equivalent to a decimal in the tenths place. The numerator of the fraction becomes the digit to the right of the decimal point.

n10=0.n\frac{n}{10} = 0.n

Examples

  • 210=0.2\frac{2}{10} = 0.2
  • 510=0.5\frac{5}{10} = 0.5
  • 910=0.9\frac{9}{10} = 0.9

Explanation

A decimal number is another way to write a fraction. When a whole is divided into 10 equal parts, each part can be written as the fraction 110\frac{1}{10} or the decimal 0.10.1. The first place to the right of the decimal point is the tenths place, representing parts out of ten. Therefore, the fraction form and decimal form for tenths are equivalent and interchangeable.

Section 3

Composing One Whole with Tenths

Property

One whole is equivalent to 10 tenths. Pairs of tenths can be added together to compose one whole, which is written as 1.01.0 or 1010\frac{10}{10}.

0.3+0.7=1.00.3 + 0.7 = 1.0
310+710=1010=1\frac{3}{10} + \frac{7}{10} = \frac{10}{10} = 1

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 1Current

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

  2. Lesson 2

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

  3. Lesson 3

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