Welcome to our lesson
on place value and whole numbers.
The goals of this video are to define counting numbers
and whole numbers, determine place value of whole numbers,
and then write whole numbers in expanded form.
In mathematics, there are different types,
or sets, of numbers.
The counting numbers, sometimes called natural numbers,
are the set of numbers as we see here, and you can see
why they're often called the counting numbers.
One, two, three, four, five, and so on
would be the numbers we use to count items.
Now whole numbers are the set of counting numbers and zero.
So whole numbers are the numbers in the set as we see here,
and again, the only differences is whole numbers
include zero, while counting numbers, don't.
Since our number system is base 10,
as we consider larger and larger counting or whole numbers,
we have to introduce place value
to distinguish between different quantities.
For example, if we were counting these items
where each square was one, we'd have a total of five,
or five in the ones place value,
which gives us the number five.
However if we wanted to count the total number
of items here, we actually start to group them in tens,
so we'd have a total of three groups of 10, so we'd have
a three in the tens column to represent the 30,
and then a two in the ones column to represent
the remaining two items, to represent the number 32.
A three in the tens column, and a two in the ones column.
Now if we wanted to count the number of items we see here
once we'd counted 10 groups of 10, that would represent
100 items, so here we see 10 groups of 10, or 100 items,
and then we have five groups of 10, or 50, so we have
a five in the tens column, and then we have three left
in the ones column to represent 153.
Now let's take a a look
at a more comprehensive place value chart.
So as we work out way from left to right using place value,
we have the ones, tens, hundreds, thousands,
10 thousands, 100 thousands, millions, 10 millions,
100 millions, and so on.
One more thing on writing large numbers,
we separate the millions and the thousands with a comma,
and the thousands and hundreds with a comma,
to help keep the digits organized.
Notice how on the place value chart,
I did include the decimal to the far right.
Because we're not going to have any digits to the right of
the decimal for whole numbers, we normally do not include
the decimal point, but the reason I wanted to include it
is the word "and" is used to represent the decimal point,
so we should use and when we say whole numbers.
So this would be eight million, three hundred two thousand,
seven hundred ninety-five.
Sometimes you'll hear people say "and,"
like seven hundred and ninety-five,
but technically that would not be correct.
So if we wanted to practice identifying place values,
this three would be in the 100 thousands place value,
the two would be in the one thousands,
or thousands, place value.
And the nine would be in the tens place value.
Let's take a look at one more example of this.
Let's go ahead and put the commas in to separate
our place values, and starting from the right,
we put a comma between every three digits here, and here.
So this would be eight hundred forty-five million,
three hundred six thousand, nine hundred seventeen.
So this four would be in the 10 millions place value.
The five would be in the one millions,
or millions place value.
And the seven would be in the ones place value.
Now sometimes you'll be asked to write numbers
in expanded form, and writing a number in expanded form
is a way to emphasize the place value of each digit.
What I mean by that is this five represents 500,
this eight represents eight tens, or 80,
and this three represents three ones, or three.
This is called expanded form of 583.
So for 12,893, this one represents one 10 thousand
or 10,000, plus two one thousands, or 2,000,
plus eight would be 800, plus this nine represents 90,
and the three represents three.
For this eight, we have the thousands, millions,
and billions, so this would be 8,000,000,000 plus,
now because there's a zero in the 100 millions place value,
we do not need to include that, so we'll have
plus 90,000,000, plus 1,000,000, plus this would be 100,000,
and the next non-zero digit is this three,
which represents 30, and then plus two.
Okay, the last thing we'll do is take a look
at how we write whole numbers in English.
We write a whole number in the same way that we say them,
using correct place value.
We separate the number in words by commas
the same way we do when we write the number.
So for example, here we have
three thousand, comma, five hundred eighty-one.
Here we have ten thousand, twenty-five,
notice the comma between the ten thousand
and the twenty-five.
And then here we have twelve million, comma,
eighty-one thousand, comma, nine hundred seventy-two.
Let's go ahead and try a couple of our own.
So we have one hundred fifty thousand,
comma, one hundred twelve.
Remember, we should not include the world "and,"
because the "and" represents a decimal point.
And in our last example, here we have
the thousands, millions, and billions.
So we have fifteen billion, eighty-five million,
two hundred five thousand,
comma, one hundred twenty-three.
And we're going to go ahead and stop here for this video.
I hope you found this helpful.