 # Expanded notation as powers of 10

Lesson

When we need to write our number using expanded notation and powers of ten, we can tackle this in two steps.

## Step 1 - Expanded  notation

The topic on expanded notation is helpful, to refresh your memory, but to summarise, it means we are breaking our number into separate 'chunks', where each chunk represents the value of each digit.  So, think of a number like $24$24. This has $2$2 tens, and $4$4 units, so would be $20+4$20+4, in expanded notation.  We make sure that we expand every digit, so thinking of place value is really helpful here.

Number Expanded notation
$3468$3468 $3000+400+60+8$3000+400+60+8
$23179$23179 $20000+3000+100+70+9$20000+3000+100+70+9

Number                                Expanded notation

$3468$3468                                  $3000+400+60+8$3000+400+60+8

$23179$23179                              $20000+3000+100+70+9$20000+3000+100+70+9

## Step 2 - Powers of ten

Our next step involves looking at each chunk of our expanded notation and considering if we can express it as a power of ten.  Powers of $10$10are new, so in the video you are able to see how we can rename $10$10, $100$100 and $1000$1000 as powers of $10$10.

$10=10=10^1$10=10=101

$100=10\times10=10^2$100=10×10=102

$1000=10\times10\times10=10^3$1000=10×10×10=103

Let's take a look at working through steps 1 and 2 in our first video.

## Step 3 - Bringing it all together in one place

In our second video, we take a number, use expanded notation, and then rename some values using the power of ten. This is where we use what we learnt in video 1, and see how we can express numbers in expanded notation, to the power of ten.

#### Worked Examples

##### Question 1

Express $2487$2487 in the expanded form using index notation. For example, $245$245 in this form is equal to $2\times10^2+4\times10^1+5\times1$2×102+4×101+5×1.

##### Question 2

Write the number expressed by: $2\times10^5+5\times10^4+6\times10^3+7\times10^1$2×105+5×104+6×103+7×101.

Note: Do not use comma separators