# 1.06 Multiplication and division by 10 and 100

Lesson

## Ideas

Can you  break a number into its parts  , using place value?

### Examples

#### Example 1

Complete the number expander for 27\,692.

a
Worked Solution
Create a strategy

Put the given number in a place value table.

Apply the idea

The complete number expander is:

b

Write 27\,692 as a number sentence.

⬚+⬚+⬚+90+2

Worked Solution
Create a strategy

Use the number expander from part (a).

Apply the idea

2 ten thousands is 20\,000, 7 thousands is 7000, and 6 hundreds is 600.

20\,000+7000+600+90+2

Idea summary

We can break a number into its parts by putting it in a place value table.

## Multiply or divide by 10 and 100

The digits in our number tell us how many units, tens, hundreds or thousands (or more) we have. Remembering that  each place is ten times larger than the place to its right  can help us when we need to multiply or divide by 10.

### Examples

#### Example 2

Fill in the boxes with the missing numbers.

6600\div⬚=66

Worked Solution
Create a strategy

Put the numbers in a place value table and see how many places the digits have moved.

Apply the idea

Put 6600 and 66 in a place value table:

The 6s in 6600 have moved 2 places to the right to get 66.

This is the same as dividing by 100.

6600 \div 100 = 66

Idea summary

When we multiply by 10, the digits move to the left one place, and our number gets bigger. We need to put a zero placeholder in the units place when we multiply by 10. When we divide by 10, our digits move to the right one place, and our number gets smaller.

When we multiply by 100, the digits move to the left two places, and our number gets bigger. We need to put zeros as placeholders in the tens and units places when we multiply by 100. When we divide by 100, our digits move to the right two places, and our number gets smaller.