Welcome to several examples
on how to round whole numbers to the nearest ten
or to the tens place value.
We'll take a look at rounding on the number line,
as well as using the formal rules for rounding.
In our first example, we're asked to round 677
to the nearest ten.
So let's first us a number line.
If we were to count be tens,
notice how 677 would fall between 670 and 680.
And now let's plot 677 on the number line.
Notice how 677 would be approximately here,
so to round 677 to the nearest ten on the number line,
we need to determine whether 677 is closer to 680 or 670.
Well, we can see it's closer to 680,
and therefore 677 rounds up to 680
when rounding to the nearest ten.
Using this method always works,
except there is one special case.
If the value happened to fall right in the middle,
the same distance from the two possible rounded values,
we always round up.
Now let's round this again
using the formal rules for rounding.
So if we begin with 677,
the formal rules tell us first to find the digit
in the rounding place value,
which is the seven in the tens place value.
Step two, we locate the digit
to the right of the rounding place value,
which is the seven and the ones place value.
So the seven and the ones place value is a decision maker.
The seven indicates whether we round up or down.
If the digit to the right of the rounding place value
is less than five, you round down.
Again, we have a seven, so this is not the case.
The second case is if the digit to the right
of the rounding place value is five or more, we round up.
So, because we have a seven in the ones place value,
which is five or more round up, so to round up the digit
in the rounding place value increases by one,
while the digit to the right becomes zero,
which means the seven in the tens place value
increases by one to eight,
and all digits to the right become zero.
So, 677 rounds to 680 when rounding to the nearest ten.
Now, let's round 243 to the nearest ten.
Use the number line and counting by tens,
243 is between 240 and 250.
243 falls approximately here on the number line.
And because 243 is closer to 240 than it is to 250
to the nearest ten, 243 rounds down to 240.
And again using the formal rules for rounding,
we begin with 243, we identify the digit in the
rounding place value, which would be the four
in the tens place value.
The digit to the right is the decision maker,
which is the three in the ones place value.
So because three is less than five, you round down.
To round down, the digit in the rounding place value
stays the same.
Notice we don't decrease it, but the digit
in the rounding place value stays the same.
So, the four in the tens stays four,
all digits to the right become zero,
the three in the ones becomes a zero, giving us 240.
Let's look at two more examples that are slightly different.
Here we are asked to round 755 to the nearest ten.
So use the number line counting by tens.
755 would be between 750 and 760,
and what's different about this example,
750 is right here in the middle.
Notice how it's the same distance from 750
as it is from 760.
So, when this is the case, the rule is that
we always round up.
So, we say that 755 rounds up to 760
when rounding to the nearest ten.
Again, using the formal rules,
we find the digit in the rounding place value,
which is the five in the tens place value.
The digit to the right indicates
whether we round up or down.
Because we have five in the ones place value,
then five is five or more, we round up,
which means the digit in the rounding place value
increases by one, so the five and the tens
increases by one to six, and all digits to the right
become zero, so the five in the ones become zero,
giving us 760.
Let's look at one last example.
We're asked to round 498 to the nearest ten.
Counting by tens, 498 is between 490 and 500.
498 would be approximately here.
Because 498 is closer to 500, than it is to 490,
498 rounds up to 500 when rounding to the nearest ten.
Using our formal rules, we begin with 498.
We begin by identifying the digit
in the rounding place value,
which is the nine in the tens place value.
The digit to the right is the decision maker,
so the eight in the ones place value indicates
whether we round up or down.
So because it is an eight and
eight is five or more, we round up.
So the digit in the rounding place value increases
by one and all the digits to the right become zero.
So this one is a little bit different,
because notice how if we increase nine to ten,
ten tens gives us 100, so we add a one to the four
in the hundreds place value, which gives us a five
in the 100s, and all the digits to the right
become zero, giving us 500.
So, if you're having difficulty rounding,
using the number line is a great way to visualize
what's happening when we round to a particular place value.
I hope you found this helpful.