Learn on PengiEureka Math, Grade 4Chapter 1: Place Value of Multi-Digit Whole Numbers

Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its right.

In this Grade 4 Eureka Math lesson from Chapter 1, students learn that each digit in a multi-digit number represents 10 times the value of the same digit one place to its right, building the place value chart up to 1 million. Through place value disks, multiplication sentences, and skip-counting practice, students explore how units like ones, tens, hundreds, and thousands relate by factors of 10. The lesson also introduces dividing to reverse the process, reinforcing the relationship between adjacent place value positions.

Section 1

Relating Place Value and Multiplication by 10

Property

The value of each place is 10 times the value of the place to its right. This means bundling 10 units of a smaller place value creates 1 unit of the next larger place value.

10×1 thousand=1 ten thousand10 \times 1 \text{ thousand} = 1 \text{ ten thousand}
10×1 ten thousand=1 hundred thousand10 \times 1 \text{ ten thousand} = 1 \text{ hundred thousand}
10×1 hundred thousand=1 million10 \times 1 \text{ hundred thousand} = 1 \text{ million}

Examples

Section 2

Multiplying by 10 by Bundling Units

Property

Bundling 10 units of a smaller place value creates 1 unit of the next larger place value. Multiplying by 10 involves bundling groups of 10.

Examples

  • To multiply 30×1030 \times 10, you can think of 3 tens multiplied by 10. This gives you 30 tens. You can bundle every 10 tens to make 1 hundred, so 30 tens is bundled into 3 hundreds, which is 300.
  • 400×10400 \times 10 is the same as 4 hundreds ×10\times 10, which equals 40 hundreds. We can bundle these 40 hundreds to make 4 thousands, or 4,000.

Explanation

This skill focuses on understanding multiplication by 10 as a process of "bundling" units. When you multiply a number by 10, you are making 10 copies of each unit. These 10 copies can then be grouped, or bundled, to form one unit of the next larger place value. This is why multiplying by 10 effectively shifts every digit one place to the left on the place value chart.

Section 3

Dividing by 10 by Unbundling Units

Property

Dividing a number by 10 is equivalent to unbundling each of its place value units into 10 units of the next smaller place value. This causes each digit to shift one place to the right, making its value 10 times smaller.

1 larger unit=10 smaller units to the right1 \text{ larger unit} = 10 \text{ smaller units to the right}
(Value)÷10=Value shifted one place to the right(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Section 4

Place Value Operations with Two Units

Property

To multiply or divide a number with multiple units by 10, apply the operation to each unit separately. For example: 10×(3 thousands 2 hundreds)=(10×3 thousands)+(10×2 hundreds)10 \times (3 \text{ thousands } 2 \text{ hundreds}) = (10 \times 3 \text{ thousands}) + (10 \times 2 \text{ hundreds}).

Examples

Find the value of 10×(2 thousands 4 hundreds)10 \times (2 \text{ thousands } 4 \text{ hundreds}).

  • 10×2 thousands =2 ten thousands10 \times 2 \text{ thousands } = 2 \text{ ten thousands}
  • 10×4 hundreds =4 thousands10 \times 4 \text{ hundreds } = 4 \text{ thousands}
  • So, the result is 2 ten thousands 4 thousands2 \text{ ten thousands } 4 \text{ thousands}, which is 24,00024,000.

Find the value of (5 ten thousands 3 thousands)÷10(5 \text{ ten thousands } 3 \text{ thousands}) \div 10.

  • 5 ten thousands ÷10=5 thousands5 \text{ ten thousands } \div 10 = 5 \text{ thousands}
  • 3 thousands ÷10=3 hundreds3 \text{ thousands } \div 10 = 3 \text{ hundreds}
  • So, the result is 5 thousands 3 hundreds5 \text{ thousands } 3 \text{ hundreds}, which is 5,3005,300.

Book overview

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Chapter 1: Place Value of Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Interpret a multiplication equation as a comparison.

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its right.

    LearnPractice
  3. Lesson 3

    Lesson 3: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units.

    LearnPractice
  4. Lesson 4

    Lesson 4: Read and write multi-digit numbers using base ten numerals, number names, and expanded form.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Relating Place Value and Multiplication by 10

Property

The value of each place is 10 times the value of the place to its right. This means bundling 10 units of a smaller place value creates 1 unit of the next larger place value.

10×1 thousand=1 ten thousand10 \times 1 \text{ thousand} = 1 \text{ ten thousand}
10×1 ten thousand=1 hundred thousand10 \times 1 \text{ ten thousand} = 1 \text{ hundred thousand}
10×1 hundred thousand=1 million10 \times 1 \text{ hundred thousand} = 1 \text{ million}

Examples

Section 2

Multiplying by 10 by Bundling Units

Property

Bundling 10 units of a smaller place value creates 1 unit of the next larger place value. Multiplying by 10 involves bundling groups of 10.

Examples

  • To multiply 30×1030 \times 10, you can think of 3 tens multiplied by 10. This gives you 30 tens. You can bundle every 10 tens to make 1 hundred, so 30 tens is bundled into 3 hundreds, which is 300.
  • 400×10400 \times 10 is the same as 4 hundreds ×10\times 10, which equals 40 hundreds. We can bundle these 40 hundreds to make 4 thousands, or 4,000.

Explanation

This skill focuses on understanding multiplication by 10 as a process of "bundling" units. When you multiply a number by 10, you are making 10 copies of each unit. These 10 copies can then be grouped, or bundled, to form one unit of the next larger place value. This is why multiplying by 10 effectively shifts every digit one place to the left on the place value chart.

Section 3

Dividing by 10 by Unbundling Units

Property

Dividing a number by 10 is equivalent to unbundling each of its place value units into 10 units of the next smaller place value. This causes each digit to shift one place to the right, making its value 10 times smaller.

1 larger unit=10 smaller units to the right1 \text{ larger unit} = 10 \text{ smaller units to the right}
(Value)÷10=Value shifted one place to the right(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Section 4

Place Value Operations with Two Units

Property

To multiply or divide a number with multiple units by 10, apply the operation to each unit separately. For example: 10×(3 thousands 2 hundreds)=(10×3 thousands)+(10×2 hundreds)10 \times (3 \text{ thousands } 2 \text{ hundreds}) = (10 \times 3 \text{ thousands}) + (10 \times 2 \text{ hundreds}).

Examples

Find the value of 10×(2 thousands 4 hundreds)10 \times (2 \text{ thousands } 4 \text{ hundreds}).

  • 10×2 thousands =2 ten thousands10 \times 2 \text{ thousands } = 2 \text{ ten thousands}
  • 10×4 hundreds =4 thousands10 \times 4 \text{ hundreds } = 4 \text{ thousands}
  • So, the result is 2 ten thousands 4 thousands2 \text{ ten thousands } 4 \text{ thousands}, which is 24,00024,000.

Find the value of (5 ten thousands 3 thousands)÷10(5 \text{ ten thousands } 3 \text{ thousands}) \div 10.

  • 5 ten thousands ÷10=5 thousands5 \text{ ten thousands } \div 10 = 5 \text{ thousands}
  • 3 thousands ÷10=3 hundreds3 \text{ thousands } \div 10 = 3 \text{ hundreds}
  • So, the result is 5 thousands 3 hundreds5 \text{ thousands } 3 \text{ hundreds}, which is 5,3005,300.

Book overview

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

Continue this chapter

Chapter 1: Place Value of Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Interpret a multiplication equation as a comparison.

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its right.

    LearnPractice
  3. Lesson 3

    Lesson 3: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units.

    LearnPractice
  4. Lesson 4

    Lesson 4: Read and write multi-digit numbers using base ten numerals, number names, and expanded form.

    LearnPractice