Learn on PengiPengi Math (Grade 4)Chapter 1: Place Value Fundamentals and Estimation

Lesson 3: Representing Multi-Digit Numbers in Different Forms

In this Grade 4 Pengi Math lesson, students learn to read and write multi-digit whole numbers in three forms: standard form using base-ten numerals, word form using number names, and expanded form as a sum of products. Part of Chapter 1 on Place Value Fundamentals and Estimation, the lesson builds core number sense skills essential for working with large whole numbers.

Section 1

Writing Numbers in Expanded Form (Sum of Products)

Property

Expanded form can be written as the sum of each digit multiplied by its place value. This shows how the value of each digit is calculated.

Examples

Section 2

Converting from Word Form to Standard and Expanded Form

Property

To convert a number from word form to standard form, identify the value of each part of the name (e.g., "three hundred thousand" becomes 300,000300,000) and sum the values. To write it in expanded form, write the sum of the values of each digit. For example, "three hundred twenty-five" is 300+20+5300 + 20 + 5.

Examples

Given "fifty-two thousand, one hundred eight":

  • Standard Form: 52,10852,108
  • Expanded Form: 50,000+2,000+100+850,000 + 2,000 + 100 + 8

Given "four hundred six thousand, seven hundred thirty":

  • Standard Form: 406,730406,730
  • Expanded Form: 400,000+6,000+700+30400,000 + 6,000 + 700 + 30

Given "nine hundred thousand, fifty-one":

  • Standard Form: 900,051900,051
  • Expanded Form: 900,000+50+1900,000 + 50 + 1

Explanation

This skill involves translating number names into their numerical representations. First, identify the place value terms like "thousand" and "hundred" to structure the number. Then, write the digits in their correct places, using zeros as placeholders for any missing values. Finally, express the number as a sum of each digit''s value to create the expanded form.

Book overview

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

Continue this chapter

Chapter 1: Place Value Fundamentals and Estimation

  1. Lesson 1

    Lesson 1: The Base-Ten System's Ten-Times Relationship

  2. Lesson 2

    Lesson 2: Reading and Writing Large Numbers

  3. Lesson 3Current

    Lesson 3: Representing Multi-Digit Numbers in Different Forms

  4. Lesson 4

    Lesson 4: Comparing Multi-Digit Numbers Place by Place

  5. Lesson 5

    Lesson 5: Comparing and Ordering Numbers in Various Forms

  6. Lesson 6

    Lesson 6: Rounding Multi-Digit Numbers to Any Place Value

  7. Lesson 7

    Lesson 7: Estimation for Sums, Differences, and Reasonableness

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Writing Numbers in Expanded Form (Sum of Products)

Property

Expanded form can be written as the sum of each digit multiplied by its place value. This shows how the value of each digit is calculated.

Examples

Section 2

Converting from Word Form to Standard and Expanded Form

Property

To convert a number from word form to standard form, identify the value of each part of the name (e.g., "three hundred thousand" becomes 300,000300,000) and sum the values. To write it in expanded form, write the sum of the values of each digit. For example, "three hundred twenty-five" is 300+20+5300 + 20 + 5.

Examples

Given "fifty-two thousand, one hundred eight":

  • Standard Form: 52,10852,108
  • Expanded Form: 50,000+2,000+100+850,000 + 2,000 + 100 + 8

Given "four hundred six thousand, seven hundred thirty":

  • Standard Form: 406,730406,730
  • Expanded Form: 400,000+6,000+700+30400,000 + 6,000 + 700 + 30

Given "nine hundred thousand, fifty-one":

  • Standard Form: 900,051900,051
  • Expanded Form: 900,000+50+1900,000 + 50 + 1

Explanation

This skill involves translating number names into their numerical representations. First, identify the place value terms like "thousand" and "hundred" to structure the number. Then, write the digits in their correct places, using zeros as placeholders for any missing values. Finally, express the number as a sum of each digit''s value to create the expanded form.

Book overview

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

Continue this chapter

Chapter 1: Place Value Fundamentals and Estimation

  1. Lesson 1

    Lesson 1: The Base-Ten System's Ten-Times Relationship

  2. Lesson 2

    Lesson 2: Reading and Writing Large Numbers

  3. Lesson 3Current

    Lesson 3: Representing Multi-Digit Numbers in Different Forms

  4. Lesson 4

    Lesson 4: Comparing Multi-Digit Numbers Place by Place

  5. Lesson 5

    Lesson 5: Comparing and Ordering Numbers in Various Forms

  6. Lesson 6

    Lesson 6: Rounding Multi-Digit Numbers to Any Place Value

  7. Lesson 7

    Lesson 7: Estimation for Sums, Differences, and Reasonableness