# 7.05 Powers of 10

Lesson

## Are you ready?

In previous years we have learned how to  multiply whole numbers by 10  and can relate the multiplication to place value. Let's review.

### Examples

#### Example 1

Complete these number sentences.

a

9\times10=⬚

Worked Solution
Create a strategy

Put the number in a place value table and move the digit one column to the left.

Apply the idea

Here is 9 in a place value table.

To multiply by 10, move each digit one column to the left. Use 0 as a placeholder.

9\times 10 = 90

b

90\times10=⬚

Worked Solution
Create a strategy

Put the number in a place value table and move each digit one column to the left.

Apply the idea

Here is 90 in a place value table.

To multiply by 10, move each digit one column to the left. Use 0 as a placeholder.

90\times 10 = 900

Idea summary

When we multiply a number by 10, each digit increases in place value by 1 place value.

We can use a place value table to multiply numbers by powers of 10.

## Multiply decimals by 10 or 100

This video looks at what happens to numbers with decimals when we multiply by 10 or 100.

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### Examples

#### Example 2

Find the value of 29.34\times100.

Worked Solution
Create a strategy

Put the decimal number in a place value table and move each digit two columns to the left.

Apply the idea

Here is 29.34 in a place value table.

To multiply by 100, move each digit two columns to the left.

29.34\times100= 2934

Idea summary

We can use a place value table to multiply decimals by powers of 10.

When multiplying by 10 each digit moves one place value to the left.

When multiplying by 100 each digit moves two place values to the left.

## Divide decimals by 10 or 100

This video looks at what happens to numbers with decimals when we divide by 10 or 100.

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### Examples

#### Example 3

Find the value of 15.8 \div 10.

Worked Solution
Create a strategy

Put the decimal number in a place value table and move each digit one column to the right.

Apply the idea

Here is 15.8 in a place value table.

To divide by 10, move each digit one column to the right.

15.8 \div 10 =1.58

Idea summary

We can use a place value table to multiply decimals by powers of 10.

When multiplying by 10 each digit moves one place value to the left.

When multiplying by 100 each digit moves two place values to the left.

## Multiply and divide decimals by larger powers of 10

This video looks at what we can do when multiplying and dividing by 10\,000.

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### Examples

#### Example 4

Find the value of 63.05\times10\,000.

Worked Solution
Create a strategy

Put the decimal number in a place value table and move each digit four columns to the right.

Apply the idea

Here is 63.05 in a place value table.

To multiply by 10\,000, move each digit four columns to the left. Use 0s as placeholders.

63.05\times10\,000=630\,500

Idea summary

For each power of 10: \, 10,\,100,\,1000,\,10\,000, when you multiply or divide by these values, each digit of your number is increased or decreased by that value, and moves up or down place value positions.

The number of place value positions each digit moves is equal to the number of zeros in the power of 10.

### Outcomes

#### VCMNA216

Multiply and divide decimals by powers of 10