Learn on PengienVision, Mathematics, Grade 5Chapter 4: Use Models and Strategies to Multiply Decimals

Lesson 1: Multiply Decimals by Powers of 10

In this Grade 5 lesson from enVision Mathematics Chapter 4, students learn how to multiply decimal numbers by powers of 10 (such as 10¹, 10², and 10³) by recognizing place-value patterns. Students discover that each time a decimal is multiplied by a power of 10, the digits shift left in a place-value chart, which is equivalent to moving the decimal point one place to the right for each power. Practice includes finding products, identifying missing exponents, and applying the concept to real-world contexts like microscope enlargements.

Section 1

The 10-to-1 Relationship Between Places

Property

In our base-10 number system, the value of each place is 10 times greater than the value of the place to its immediate right.

Value of a place=10×Value of the place to its right \text{Value of a place} = 10 \times \text{Value of the place to its right}

Examples

Section 2

Verifying the Direction of the Decimal Shift

Property

When multiplying a positive number by a power of 10 (a value greater than 1), the product must be greater than the original number. Moving the decimal point to the right increases the value of the number, while moving it to the left decreases the value.

Check: Is Original Number×Power of 10>Original NumberOriginal \ Number \times Power \ of \ 10 > Original \ Number?

Section 3

Representing Powers of 10 with Exponents

Property

A power of 10 can be written in exponential form as 10n10^n, where the base is 10 and the exponent nn indicates the number of times 10 is used as a factor. The value of the exponent nn is equal to the number of zeros in the standard form of the number.

10n=10×10×⋯×10⏟n factors10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ factors}}

Examples

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Chapter 4: Use Models and Strategies to Multiply Decimals

  1. Lesson 1Current

    Lesson 1: Multiply Decimals by Powers of 10

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  2. Lesson 2

    Lesson 2: Estimate the Product of a Decimal and a Whole Number

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  3. Lesson 3

    Lesson 3: Use Models to Multiply a Decimal and a Whole Number

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  4. Lesson 4

    Lesson 4: Multiply a Decimal and a Whole Number

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  5. Lesson 5

    Lesson 5: Use Models to Multiply a Decimal and a Decimal

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  6. Lesson 6

    Lesson 6: Multiply Decimals Using Partial Products

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  7. Lesson 7

    Lesson 7: Use Properties to Multiply Decimals

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  8. Lesson 8

    Lesson 8: Use Number Sense to Multiply Decimals

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Lesson overview

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Section 1

The 10-to-1 Relationship Between Places

Property

In our base-10 number system, the value of each place is 10 times greater than the value of the place to its immediate right.

Value of a place=10×Value of the place to its right \text{Value of a place} = 10 \times \text{Value of the place to its right}

Examples

Section 2

Verifying the Direction of the Decimal Shift

Property

When multiplying a positive number by a power of 10 (a value greater than 1), the product must be greater than the original number. Moving the decimal point to the right increases the value of the number, while moving it to the left decreases the value.

Check: Is Original Number×Power of 10>Original NumberOriginal \ Number \times Power \ of \ 10 > Original \ Number?

Section 3

Representing Powers of 10 with Exponents

Property

A power of 10 can be written in exponential form as 10n10^n, where the base is 10 and the exponent nn indicates the number of times 10 is used as a factor. The value of the exponent nn is equal to the number of zeros in the standard form of the number.

10n=10×10×⋯×10⏟n factors10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ factors}}

Examples

Book overview

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

Continue this chapter

Chapter 4: Use Models and Strategies to Multiply Decimals

  1. Lesson 1Current

    Lesson 1: Multiply Decimals by Powers of 10

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  2. Lesson 2

    Lesson 2: Estimate the Product of a Decimal and a Whole Number

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  3. Lesson 3

    Lesson 3: Use Models to Multiply a Decimal and a Whole Number

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  4. Lesson 4

    Lesson 4: Multiply a Decimal and a Whole Number

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  5. Lesson 5

    Lesson 5: Use Models to Multiply a Decimal and a Decimal

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  6. Lesson 6

    Lesson 6: Multiply Decimals Using Partial Products

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  7. Lesson 7

    Lesson 7: Use Properties to Multiply Decimals

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  8. Lesson 8

    Lesson 8: Use Number Sense to Multiply Decimals

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