# Standard Notation and Expanded Notation

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A number can be written in three ways:
We have Standard Form, Expanded Form, and Words.
Now, Standard Form is our typical, concise
method for writing a number using digits.
Expanded Form, now this form
uses place value to show the connection between
the location of the digit within the number
and then what it really means.
So, for example, if I take 382
and I want to expand it out
I would need to know that 3 is in the hundreds position
the 8 is in the tens position,
and 2 is in the ones position
so I could find this expanded form of 300+80+2
and the third form is words.
We want to be able to take a number like 382
and write it down in words
and we often find this useful if we are writing a check
or, perhaps, having to write down the amount
that we just spent in a checkbook or something like that.
So, we use these three different forms
of writing a word for different uses.
Now in this video, I'm going to focus on the first two forms
Standard Form and Expanded Form
and converting from one to another
I'm going to make another video that describes how to write a number in words
and then change the number back from words into Standard Form.
So, take a look for that one.
Alright, so starting out, we want to
convert this number that's in Standard Form
and we want to convert it to Expanded Form.
So what we are going to do is use our idea of "place value"
and so 2 is in the thousands position,
I would start out by writing that I have 2 thousands
and...so "plus" ...
I have 0 in the hundreds position
plus I have 3 in the tens position
and I have 5 in the ones position.
Now we often don't stop here.
Just writing it in words isn't enough.
We actually want to write out "2 thousand"
What this means is that we have 2 groups of 1000
so 2 times 1000 will give me 2000.
Some people can go right from 2 thousand to writing it down and that's perfectly fine.
Now, if you have 0 hundreds
You're really saying that you have 0 groups of 100.
and 0 times any number is just zero.
So, it's like adding 0.
Then I have 3 tens, so I have
3 groups of 10 which is 30.
and then I have 5 groups of 1
which is 5 times 1 which is 5.
Now this is called our expanded version.
The only thing we could do to simplify this just slightly
is to notice that I have 0.
When I add 0 to anything it doesn't change that number, so
I can actually remove the 0 and say
The Expanded Form is 2000 + 30 + 5.
And this would be my answer in Expanded Form.
Now I'm going to do the same thing with another example
18, 951 and I want to expand it out.
So, going back to the idea of place value, I have
1 is in the "ten thousands" position, so I have 1 ten thousand.
and I have 8 in the "thousands" position
so I have 8 thousand
9 is in the "hundreds" position, so I have 9 hundreds
5 is in the "tens" position, so "plus" or add
5 tens and I have 1 in the ones position.
If i want to write this down in Expanded form using
using digits, 1 ten thousand is 10,000 plus 8,000
so 8 times 1,000 is 8,000
plus 9 hundreds so 9 times 100 is 900.
5 times 10 or 5 "tens" is 50.
and then 1 "ones" is 1.
So, this would be my Expanded Form of the number 18,951.
Now we also want to go in the opposite direction.
So instead of taking a number in Standard Form and expanding it out,
what happens if I give you a number
or we receive a number that's in Expanded Form and
we want to go backwards and write it in Standard Form?
So, the last two examples...That's what we're going to do here.
You'll notice that I have "2 hundreds + 4 tens + 9 ones"
Now one thing you can do is say, okay, I have 2 groups of 100
which is 200.
plus I have 4 groups of ten or 4 "tens" which is 40.
and I have 9 ones
So, 9 groups of 1... 9 times 1 is 9.
But I can't stop here because this is still in Expanded Form.
So, I'd have to add these together.
200 plus 40 plus 9 is 249.
And this would be my answer in Standard Notation.
Another way to do this, and let's take a look at the second example,
1 thousand + 8 hundreds + 3 ones
Okay, let's just take a look at place value.
I know that my largest place value is my "thousands"
So, I'm going to write down 4 separate dashes to
to indicate my places. On the far right, I have
my "ones," then I have my "tens", "hundreds", and thousands" and since I have
1 thousand, I'll put the 1 in the thousands position.
I have 8 in the hundreds position.
So, I could put the 8 here.
and I have 3 ones, so notice I'll put 3 on the far right in the first little blank.
Now, you'll notice that I don't have any "tens"
I have zero tens here, so I'll need to put a place holder 0
to indicate that I don't have any "tens" at all.
and the number in Standard Form
Would be 1,803.