Learn on PengiEureka Math, Grade 5Chapter 1: Multiplicative Patterns on the Place Value Chart

Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.

Grade 5 students learn to use exponents to represent place value units, exploring how repeated multiplication by 10 can be expressed using powers of 10. This Eureka Math lesson builds understanding of the relationship between exponents and place value, including how multiplying or dividing by powers of 10 shifts the decimal point. Students work with a powers of 10 chart and place value models to identify and explain patterns in decimal placement.

Section 1

Representing Powers of 10 with Exponents

Property

A power of 10 can be written in exponential form as $10^n$ , where the base is 10 and the exponent $n$ indicates the number of times 10 is used as a factor. The value of the exponent $n$ is equal to the number of zeros in the standard form of the number.

10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ factors}}

Examples

Section 2

Multiplying and Dividing Numbers by Powers of 10

Property

To multiply by a power of 10, move the decimal point to the right.

a \times 10^n

To divide by a power of 10, move the decimal point to the left.

a \div 10^n

Examples

$4.53 \times 10^3 = 4.53 \times 1,000 = 4,530$
$67 \div 10^2 = 67 \div 100 = 0.67$
$18.9 \div 10^3 = 18.9 \div 1,000 = 0.0189$

Explanation

When multiplying a number by a power of 10, such as $10^n$ , you move the decimal point $n$ places to the right. When dividing a number by a power of 10, you move the decimal point $n$ places to the left. The exponent tells you exactly how many places to shift the decimal. You may need to add placeholder zeros if there are not enough digits.

Section 3

Identify Patterns in Powers of 10 Sequences

Property

In a sequence generated by powers of 10, each term is found by repeatedly multiplying or dividing the previous term by the same power of 10 (e.g., $10^1$ , $10^2$ , $10^3$ ).

Examples

Book overview

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Chapter 1: Multiplicative Patterns on the Place Value Chart

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Lesson 1
Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 2
Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 3Current
Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.
Learn Practice
Lesson 4
Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Representing Powers of 10 with Exponents

Property

10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ factors}}

Examples

Section 2

Multiplying and Dividing Numbers by Powers of 10

Property

To multiply by a power of 10, move the decimal point to the right.

a \times 10^n

To divide by a power of 10, move the decimal point to the left.

a \div 10^n

Examples

$4.53 \times 10^3 = 4.53 \times 1,000 = 4,530$
$67 \div 10^2 = 67 \div 100 = 0.67$
$18.9 \div 10^3 = 18.9 \div 1,000 = 0.0189$

Explanation

Section 3

Identify Patterns in Powers of 10 Sequences

Property

In a sequence generated by powers of 10, each term is found by repeatedly multiplying or dividing the previous term by the same power of 10 (e.g., $10^1$ , $10^2$ , $10^3$ ).

Examples

Book overview

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

Continue this chapter

Chapter 1: Multiplicative Patterns on the Place Value Chart

Back to Eureka Math, Grade 5

Lesson 1
Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 2
Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 3Current
Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.
Learn Practice
Lesson 4
Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.
Learn Practice

Overview

Lesson overview

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

Overview

Section 1

Representing Powers of 10 with Exponents

Property

10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ factors}}

Examples

Section 2

Multiplying and Dividing Numbers by Powers of 10

Property

To multiply by a power of 10, move the decimal point to the right.

a \times 10^n

To divide by a power of 10, move the decimal point to the left.

a \div 10^n

Examples

$4.53 \times 10^3 = 4.53 \times 1,000 = 4,530$
$67 \div 10^2 = 67 \div 100 = 0.67$
$18.9 \div 10^3 = 18.9 \div 1,000 = 0.0189$

Explanation

Section 3

Identify Patterns in Powers of 10 Sequences

Property

In a sequence generated by powers of 10, each term is found by repeatedly multiplying or dividing the previous term by the same power of 10 (e.g., $10^1$ , $10^2$ , $10^3$ ).

Examples

Book overview

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

Continue this chapter

Chapter 1: Multiplicative Patterns on the Place Value Chart

Back to Eureka Math, Grade 5

Lesson 1
Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 2
Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.
Learn Practice
Lesson 3Current
Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.
Learn Practice
Lesson 4
Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.
Learn Practice

Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.

Property

Examples

Property

Examples

Explanation

Property

Examples

Chapter 1: Multiplicative Patterns on the Place Value Chart

Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.

Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

Lesson overview

Property

Examples

Property

Examples

Explanation

Property

Examples

Chapter 1: Multiplicative Patterns on the Place Value Chart

Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.

Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 3: Use exponents to name place value units, and explain patterns in the placement of the decimal point.

Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.