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Purcell Math

Math Methods Grades 4-8

Multiplication and Division by 10, 100, and 1000

Introduction

Understanding how to multiply and divide by powers of 10 is a foundational skill in math, especially for simplifying calculations and understanding place value. Let’s walk through some examples and break down the steps so you can see the pattern.

Multiplication by 10, 100, and 1000

A percent is simply a way to express a number as a part of 100. So, when we say “30 percent,” we’re really talking about the fraction 30/100, or 0.3. Here’s a practical look at how percents work in everyday math.

Example 1:
What is 76 × 10?
Solution:
Write the original number: 76
Since we’re multiplying by 10, add one zero to the end of the number.
Result: 76 becomes 760

Example 2:
What is 24 × 100?
Solution:
Write the original number: 24
Since we’re multiplying by 100, add two zeros to the end of the number.
Result: 24 becomes 2400

Example 3:
What is 360 × 1000?
Solution:
Write the original number: 360
Since we’re multiplying by 1000, add three zeros to the end.
Result: 360 becomes 360,000

Division by 10, 100, and 1000

When dividing by 10, 100, or 1000, you move the decimal point to the left instead. This reduces the value of the number by powers of 10.

Example 1:
What is 1234 ÷ 1000?
Solution:
Start with the original number: 1234
Since we’re dividing by 1000, move the decimal three places to the left.
Result: 1.234

Example 2:
What is 63 ÷ 100?
Solution:
Start with the original number: 63
Move the decimal two places to the left (for division by 100).
Result: 0.63

Example 3:
What is 25 ÷ 10,000?
Solution:
Start with 25
Move the decimal four places to the left (for division by 10,000).
Result: 0.0025

Key Takeaway

When multiplying by 10, 100, or 1000, simply add zeros to the end of the number for each power of 10. When dividing, move the decimal to the left by the number of zeros in the divisor. These quick steps make it easy to calculate with large powers of 10.

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