Learn on PengienVision, Mathematics, Grade 5Chapter 1: Understand Place Value

Lesson 1: Patterns with Exponents and Powers of 10

In this Grade 5 enVision Mathematics lesson from Chapter 1, students learn how to write numbers using exponents and powers of 10, including expressing repeated multiplication such as 10 × 10 × 10 as 10³. Students explore the pattern between exponents and the number of zeros in a product, then apply this understanding to solve problems involving expressions like 5 × 10³ and 9 × 10⁶.

Section 1

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

Section 2

Multiplying Whole Numbers by Powers of 10

Property

To multiply a whole number by a power of 10, annex (add) the same number of zeros to the end of the whole number as the value of the exponent.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

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

Section 2

Multiplying Whole Numbers by Powers of 10

Property

To multiply a whole number by a power of 10, annex (add) the same number of zeros to the end of the whole number as the value of the exponent.

Examples