Ordering large numbers: least to greatest | 4th grade math (TX TEKS) | Khan Academy

- [Instructor] So we have
two groups of numbers here.

One I wrote in this yellow color

and one in this purple color.

And what I want you to
do is pause this video

and for each of these groups,

the yellow group and the purple group,

I want you to order them
from least to greatest.

So pause the video and
have a shot of that.

Okay, now let's work on this together.

So the way that I would order numbers,

whether I'm going from least to greatest

or greatest to least,

is I would look at the same place value.

Now I'd start at the most significant,

the largest place value
that I have in either,

in any of the numbers,
and I would see which one

has the largest digit there.

So if I go, all of these are
in the hundred thousands.

They all have a hundred
thousand place here,

and we see that they're all seven.

They're all 700,000s.

So they're not looking
too different there.

Then we could go to the
ten-thousandths place.

So this one has nine
10-thousands, nine 10-thousands,

nine 10-thousands.

So they're both looking pretty,

all three of them, I should say,

are looking pretty similar there.

All right, now let's go
to the thousands place.

I have a zero, a zero,
and now I have a one.

So this one over here, the 791,000,

this is actually going to be the largest

of all of these three numbers.

So I'm gonna order from least to greatest.

So I know that this one's
going to be in third place.

So 791,000, this is the greatest.

It's going to be greater than
whatever we put before it.

Now it's a competition between these two

for whichever one is least.

So let's go to the next place value.

The next place value.

We go to the hundreds place.

They both have four hundreds,

so they are looking similar so far.

Then we go to the tens place.

This has zero tens.

This has five tens.

So this one over here is larger five tens.

This says zero tens.

So actually, I could have just,

it's already written in
order from least to greatest.

I could have just done that,

but let me just write it this way again.

790,450

and 790,408 is less than,

you could think of it as
the small end of the sign,

points of the smaller number is less

than 790,450, which is less than 791,000.

Now let's do these numbers here.

Okay, so it might be tempting
to look at the first digit

and say, "Oh, I have a nine there,

and then I have a three and a three.

Nine is bigger than three.

This must be the largest number."

But then you have to be careful.

You have to look at place value.

If we pay careful attention,

this nine is in a much
less significant place.

One way to think about
it is this is 900,000s.

While here, these threes,

these are in the 100 millions.

So these are much, much more significant.

So we already know that this 900,000,

it doesn't even get into the millions,

much less the tens of millions
or the hundreds of millions.

This is going be the
smallest of the numbers.

So let me just write it over here.

So it's 986,700.

This is going to be
smaller than the other two.

But now let's figure out a competition

between these two for which one is greater

so we can go to the next place value.

We can go to the 10 millions.

They're the same.

We could go to the millions.

They're still the same.

We can go to the hundred thousands.

They're still the same.

If one way to think about it,

if you wanted to rewrite
this first number,

you could have written
it as 0, 0, 0, then a 9

if you wanted to compare it directly.

Obviously, most people don't
write numbers like that,

but we're now in the a
hundred thousands place,

which was right over there.

That said zero for every
other place before that.

But they're still looking similar.

All right, let's go to
the ten thousandths place.

Still looking similar,

but then we go to the thousandths place

and the number on the right

is the larger of them.

So we can say, actually
these were already written

from least to greatest.

So this is going to be,

this number is less than this number,

376, 392,109,

which is less than this number,

376,394,400,

and we're done.