# Rounding Whole Numbers

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We're definitely going to know these places...
We won't talk about decimals just yet.
Then the "hundreds"...
Then the "thousands"...
Now at this point you don't have to put a comma...but you can.
But...if your're number contains 5 digits or more
your are required to put a comma. That's the rule.
If you don't follow it You'll be marked wrong.
After "ten thousands" is the "hundred thousands"...
And then the "millions" digit...
And then the "ten millions" digit...
And so on. That's high enough for our purposes.
Now, suppose if you would that I asked you...
to "round" a number.
Here's how it's done...
You'll need to know WHICH digit to round TO.
In this case I'll ask you to round this number
to the nearest "tens" digit.
Here it is. So everything after that digit...
is going to be a zero.
So we have to ask ourselves...
Is our rounded answer going to be 560 or 570?
We decide between those using the NEXT
digit AFTER the "tens" (in this case)
The digit AFTER the one we asked you to round to....
In this case...that "5" can only be...
one of the following ten numerals. Ten is not one of them is it? Zero is though.
And those ten are divided into two groups...
the lower half of the numbers...0, 1, 2, 3, or 4
and the higher half of the numbers... 5, 6, 7, 8, or 9
Note that "5" is not in the middle but actually...
he's in the higher group. So...
That means we need to round UP.
And the answer 565 (rounded to the nearest ten) will correctly be... 570.
Let's try another example...
Let's round this number to the nearest "thousand".
First thing you do is find the "thousand" digit...
There it is.
That means everything after that will end up being a zero.
And the rounded answer will either be...
267,000 or 268,000
Remember who decides? ... The NEXT digit is who!
And the NEXT didit is the "3".
Now he's in the lower group isn't he? So...
In this case we keep the "7" and the (rounded) answer is 267,000.
Note we never go down. It's either "up" or "stay the same".
Let's do yet another one...
In this case we will round the SAME number...
Only this time... to the nearest "one hundred".
So... It's either going to be...
267,300 or 267,400. Note a different "round" digit yields different answers.
Who's going to decide? The NEXT digit!
That NEXT digit is different this time. In THIS case...
It's the 6. (Since we're rounding to the nearest "hundred".)
6 is certainly in the "upper" group (more than half way).
So the (rounded) answer ends up being... 267,400
Got the idea?
Now we don't just round for the sake of rounding...
We round to make problems easier. For instance...
Suppose I asked you to add these numbers. You could but It would be somewhat hard.
And what if we only needed an "estimate" of the sum.
You wouldn't add them up and THEN round because then you...
would have already have had to do the work.
What you would do is round each of the numbers FIRST...
This would make the problem easier (because of all the zeros).
In this case we'll round to the nearest 100 (since it makes the problem the easiest).
Because ALL of the numbers have hundreds.
294 rounds to 300, 613 rounds to 600, and 1671 rounds to 1700. (hundreds now)
This makes it WAY easier to add them up (because zeroes are easy to deal with).
And the estimated sum is... 2600
This method is way faster and easier
In fact please note... the real answer is 2578 (which puts us pretty darn close).
Now if you need to be exact then this method won't be useful. But if you don't...
then Use "rounding BEFORE adding" to make your work easier.
Again note that we rounded each number FIRST
and THEN added. round FIRST...THEN add!
Let's do a more realistic example... Let's estimate this distance by "rounding".
If the distance from Germantown to Richmond is 94 miles and...
the distance from Richmond to Atlanta is 379 miles and...
the distance from Atlanta to Miami is 281 miles.
Now if I wanted an estimate of how far it is from Germantown to Miami...
I guess the easiest way would be to round each FIRST and then add...
Now if we choose to round to 100's then... 94 rounds to 100 ...
379 rounds to 400 and 281 rounds to 300.
Note that I picked to round to the 100's. If they don't specify then...
pick the highest digit that all the numbers contain. That makes it the easiest!
It is very easy now. The estimated distance is...
about... 800 miles from Germantown to Miami. It's important to know how to estimate.
Let's do just ONE MORE...
I see Joe has the following test scores: 59, 74, 89, and 85 on his math tests.
Let's estimate the total. Since they all have 10's digits...
I'll round each to the nearest tens "digit" to get an approximate sum...
Rounding each to the nearest ten FIRST yields...
60, 70, 90, and 90. And it's much easier to add them now...
They add up to 310.
OK... Now go try the homework! Get Busy!