# 1.05 Multiply and divide by 10; the powers of 10

Lesson

## Ideas

Let's remember how the numbers are affected when we  multiply and divide by  10.

### Examples

#### Example 1

Find 8\times 10.

Worked Solution
Create a strategy

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

Apply the idea

Here is 8 in a place value table:

When we multiply by 10, the 8 moves to the left in the table and we use 0 as a place holder.

8 \times 10 = 80

Idea summary

When we are multiplying our number by 10, it's the same as moving each of the digits to the left one place value position. Doing this will mean we also add a zero to the number as a zero place-holder.

We do the opposite for division, so when we divide by 10, we move each of the digits one place value to the right, just like this example.\begin{aligned} 230 \times 10 &= 2300 \\ 2300 \div 10 &= 230 \end{aligned}

## Powers of 10

### Examples

#### Example 2

Fill in the boxes with the missing numbers.

a

8 \times ⬚ =800

Worked Solution
Create a strategy

Put the numbers in a place value table.

Apply the idea

Here are 8 and 800 in a place value table.

The 8 moved 2 places to the left to get 800. This is the same as multiplying by 100.

8\times 100 = 800

b

8 \times ⬚ =80

Worked Solution
Create a strategy

Put the numbers in a place value table.

Apply the idea

Here are 8 and 80 in a place value table.

The 8 moved 1 place to the left to get 80. This is the same as multiplying by 10.

8\times 10 = 80

Idea summary

We can use place a value table to find the power of 10 being multiplied.

## Large powers of 10

### Examples

#### Example 3

Solve 13\,000 \div 100.

Worked Solution
Create a strategy

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

Apply the idea

Here is 13\,000 in a place value table.

To divide it by 100, all the digits move to the right two columns in the place value table.

13\,000 \div 100 = 130

Idea summary

When we are multiplying our number by a power of 10, it's the same as moving each of the digits to the left in a place value table. Doing this will mean we also add zeros to the number as place-holders.

We do the opposite for division, so when we divide by a power of 10, we move each of the digits to the right in a place value table.\begin{aligned} 230 \times 100 &= 23\,000 \\ 2300 \div 100 &= 23 \end{aligned}

### Outcomes

#### VCMNA209

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations