Okay, let's talk about rounding.
Rounding is something
that I don't think a lot
of people understand,
exactly kind of what's
going on behind the scenes
when we round.
A lot of times teachers just tell you,
well look at the number
to the right of it,
and if it's five or higher, you round up,
and if it's four of
lower, it stays the same.
But I'd like to show you
what's really happening,
kind of behind the scenes, of rounding.
So, let's take this example problem.
We have 2,875 to the nearest thousand.
Here's the way I want
you to think about it,
you owe me $2,875, and
you show up and you say,
hey, listen, I've only
got thousand dollar bills,
let's just pretend that these exist,
only got thousand dollar bills,
and I say, ah, well great,
alright, well then, we
are going to round it,
so you're going to have to pay
me to the nearest thousand.
So, basically what we're asking,
or what we're working at is,
if this is a number line.
And here is 2,000, and here is $3,000,
first of all, in the middle
is going to be 2,500.
Okay, and literally what I'm
asking is which one is this,
$2,875 closest to?
Is it closer to 2,000?
Or is it closer to 3,000?
So the best way to do it, and
you'll see on our class notes,
that I have you prove
it using a number line,
this is what I mean by that.
So the best way to do it is to
plot it, put your 2,000, your 3,000,
we can also underline the
place value and that will help
tell you what these numbers should be.
Notice that I'm jumping one number here,
so 2,000 to 3,000, or I'm
jumping a whole thousand.
And I know that because it
tells me the nearest thousand.
So I'm going to plot this
in on my number line,
so I know that 2,500 is here,
well, 2,800, let's see,
this would be about 2,600,
2,700, 2,800, 2,900.
So I know that 2,875 is going
to be about right there.
So again, now I'm asking
myself is it closer to
2,000 or 3,000?
Well we can clearly see
it's closer to 3,000.
So, 2,875 rounded to the nearest thousand,
would be 3,000.
Let's talk about that same
number rounded to the nearest 10.
Again, we're dealing with 2,875.
So I'm going to underline my,
the number that's in the 10's place.
So I know this is the one's place.
That's the 10's place.
So when I draw my number line,
because this is telling
me to the nearest 10,
I need to jump 10.
So that means that this
is going to be 2,870,
this is going to be 2,880.
And in the very middle
is going to be 2,800,
what's halfway between 70 and 80?
75.
Oh, it just so happens that in this case,
my number is exactly in the middle.
So if you owe me $2,875,
and you only have $10 bills,
I'm going to tell you that I want $2,880
because, since it's in the middle,
or on the right hand side,
it's closer to 2,880.
So, 2,875 rounded to the
nearest 10 would be 2,880.
Hope that helps.
