---
title: "Patterns with Powers of Ten"
description: "Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000"
canonical: https://lightmysky.com/learn/mathematics/patterns-with-powers-of-ten-mt_HLUqHJ9Y7n
source: https://lightmysky.com/learn/mathematics/patterns-with-powers-of-ten-mt_HLUqHJ9Y7n.md
retrieved: 2026-10-19
---

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# Patterns with Powers of Ten

Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)

Subject: Mathematics · Area: Number Representation & Place Value · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/patterns-with-powers-of-ten-mt_HLUqHJ9Y7n

## Ready when they can

- Write 10⁴ = 10,000 and explain the exponent means four factors of 10
- Explain why 3.4 × 10² = 340 by describing the decimal shift
- Predict 2.56 × 10³ without calculating and explain the pattern

## Lesson: Patterns with Powers of Ten

You already know that multiplying by 10 shifts every digit one place to the left. A power of ten is a short way to write repeated tens. 10³ means three factors of 10 multiplied together: 10 × 10 × 10.

*(drawing: 10¹ = 10, 10² = 100, 10³ = 1,000, 10⁴ = 10,000. The exponent tells you how many zeros.)*

**Example.** 3.4 × 10² has an exponent of 2, so the decimal point moves two places to the right: 3.4 becomes 340.

**Tip.** Count the exponent to know how many places to move the decimal point, or how many zeros a whole number gets. 10⁵ means five places, or five zeros.

**Recap.** The exponent on a power of ten tells you how many places the decimal point moves, or how many zeros the number gets.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Place Value × 10 and ÷ 10](https://lightmysky.com/learn/mathematics/place-value-10-and-10-mt_EDgw64OmfA)
- [Multiplying and dividing by 10, 100, and 1000](https://lightmysky.com/learn/mathematics/multiplying-and-dividing-by-10-100-and-1000-mt_LlMl2PbaZe)

## Opens up

- [Laws of Exponents](https://lightmysky.com/learn/mathematics/laws-of-exponents-mt_UjNba32kkz)