NZ Level 3
Expanded notation and expanded form
Lesson

## Expanding our number

We've seen before how we can build, or construct, numbers up to $50000$50000, where place value helped us understand how much each digit was worth. Now we're going to look at how we can start with a large number, and break it down into its parts. We will look at the value each digit has, depending on where it is located in the number.

Remember how we used base 10 blocks to compare numbers? It's a little like that, but this time, where the digit is located tells us what it is worth.

### solving problems

Now that we've seen how to deconstruct and construct numbers, let's use this to solve some problems. We left Video 1 seeing how 30 470 could be written as 3 047 if we left out our zero placeholder. We'll start Video 2 by looking at one other way you might build 30 470.

Then we move on to using the value of each digit to solve some addition and subtraction problems. We also look at multiplying by multiples of 10, and see what this means when we think of place value.

Remember!

Each time we look at a number, the value of the digit depends on where it is in the number. Place value rules tell us the value, and we use this every time we work out number problems.

#### Worked Examples

##### Question 1

Express the following number in expanded form:

$33294$33294.

##### Question 2

Write the following as a single number:

$1\times10000+9\times1000+6\times10$1×10000+9×1000+6×10.

Note: Do not use comma separators

##### Question 3

Express $36969$36969 in expanded form. For example, $245$245 in expanded form is equal to $200+40+5$200+40+5.

### Outcomes

#### NA3-3

Know counting sequences for whole numbers.

#### NA3-4

Know how many tenths, tens, hundreds, and thousands are in whole numbers.