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Lesson 5: Comparing decimal place values

# Powers of ten: FAQ

## What is a power of ten?

A power of ten is when you multiply ten by itself a certain number of times. For example, 10, squared means to multiply ten by itself twice, resulting in 100.
Try it yourself with this exercise:

## What does it mean to multiply and divide by $10$10, $100$100, or $1{,}000$1, comma, 000?

When you multiply a number by 10, 100, or 1, comma, 000, you're making it ten, one hundred, or one thousand times larger.
When you divide a number by 10, 100, or 1, comma, 000, you're making it ten, one hundred, or one thousand times smaller.
Try it yourself with this exercise:

## How do I multiply and divide a decimal by $10$10, $100$100 or $1{,}000$1, comma, 000?

When you multiply a decimal by 10, 100 or 1, comma, 000, you're effectively shifting the decimal point to the right.
• When you multiply by 10, the decimal point moves one place to the right. For example, 2, point, 3, times, 10, equals, 23.
• When you multiply by 100, the decimal point moves two places to the right. For example, 2, point, 3, times, 100, equals, 230.
• When you multiply by 1000, the decimal point moves three places to the right. For example, 2, point, 3, times, 1, comma, 000, equals, 2, comma, 300.
When you divide a decimal by 10, 100 or 1, comma, 000, you're effectively shifting the decimal point to the left.
• When you divide by 10, the decimal point moves one place to the left. For example, 23, divided by, 10, equals, 2, point, 3.
• When you divide by 100, the decimal point moves two places to the left. For example, 230, divided by, 100, equals, 2, point, 3.
• When you divide by 1, comma, 000, the decimal point moves three places to the left. For example, 2, comma, 300, divided by, 1, comma, 000, equals, 2, point, 3.
Try it yourself with these exercises:

## How do I multiply by a power of ten?

To multiply by a power of ten, you follow the same rules as before. For example, to multiply by 10, squared, you multiply by 100, and to multiply by 10, cubed, you multiply by 1, comma, 000.
Try it yourself with this exercise:

## Why do I need to know how to multiply and divide by powers of ten?

Multiplying and dividing by powers of ten is a useful skill in a lot of different situations. For example, you might use it when converting between metric units or when calculating percentages.