Welcome to a 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 difference is
whole numbers include zero while counting numbers
don't. Since our number system is base ten,
as we consider a larger and larger counting our whole numbers,
we have to introduce place value to distinguish between different quantities.
For example, if we were counting these items, or 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'd actually start to group them
in tens, so we'd have a total of
three groups of ten. So we'd have a three
in the tens column to represent the thirty, and then a two in the ones column to represent
the remaining two items, to represent the number thirty-two,
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've counted ten groups of ten, that would represent
one hundred items. So here we see ten groups of ten,
or one hundred items, and then we have five groups of ten, or fifty.
So we have a five in the tens column, and then we have three left in the ones column,
to represent one hundred fifty-three. Now let's take a look at a more comprehensive place value chart.
So as we work our way from left to right using place value, we have the ones,
tens, hundreds, thousands,
ten thousands, hundred thousands, millions,
ten millions, hundred millions, and so on. One more thing when running 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 in 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 shouldn't use
and when we say a 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 hundred 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.
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 ten 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 five hundred.
This eight represents eight tens, or eighty.
And this three represents three ones or three.
This is called expanded form of five hundred eighty-three.
So for twelve thousand, eight hundred ninety-three, this one, represents
one ten thousand or ten thousand. Plus
two one thousands, or two thousand.
Plus eight would be eight hundred.
Plus this nine represents ninety,
and the three represents three. For this eight,
we have the thousands, millions, and billions. So this would be
eight billion. Plus, now because there's a zero in the hundred millions
place value, we do not need to include that. So we'll have plus
ninety million,
plus one million,
plus this would be one hundred thousand.
And the next non-digit is this three, which represents thirty,
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 our 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 and try a couple of our own. So we have one hundred fifty thousand,
comma, one hundred twelve. Remember we should not include the word and, because the word and represents
a decimal point.
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.