We're asked to round
2,998 to the nearest ten
as well as to the nearest ten thousand.
We'll be discussing how to
round using the number line
as well as how to use the
formal rules surrounding
outlined here below.
Let's begin by rounding
2,998 to the nearest ten
using the number line.
The first thing we need to recognize is,
if we are counting by tens,
2,998 would be between
2,990 and 3,000.
And, of course, in the
middle we would have 2,995.
The next step is to plot the given number
on this number line.
Well 2,998 would be approximately here.
So to round 2,998 to the nearest ten,
now we just need to determine
whether the given number
is closer to 3,000 or 2,990.
Well we can easily see that
2,998 is closer to 3,000
than it is to 2,990.
And therefore, 2,998 rounds up to 3,000
when rounding to the nearest ten.
So this method of rounding
when using the number line
always works, though
there is one special case.
If the given number happened
to be right in the middle
between the two possible rounded values,
for example, if the
given number was 2,995,
the rule is we always round up.
Now let's also round 2,998
using our formal rules surrounding.
So, step one, we find the digit
in the rounding place value.
Because rounding to the nearest ten,
the rounding place value
is the nine in the tens place value.
Step two, we look at
the digit to the right
of the rounding place
value which in our case
is the eight in the ones place value.
So if the digit to the
right is less than five,
we round down, if it's
five or more, we round up.
To round up, the digit in
the rounding place value
increases by one, all digits
to the right become zero.
So we're told to increase the
rounding place value by one.
But notice here it's a nine
and because nine plus one is ten
and ten tens is equal to 100,
we perform an exchange
and add a one to the nine
in the hundreds place value.
But now we have ten hundreds,
and because ten hundreds
is equal to 1,000,
we end up adding a one to the two
in the thousands place
value which gives us three
and then all digits to
the right become zero.
So we have a zero in the hundreds,
a zero in the tens and a zero in the ones
which gives us a rounded value of 3,000.
So notice how in this case,
the formal rules are a little tricky,
but using the number line
is very straight forward.
Now let's round the same number
to the nearest ten thousand.
So using the number line,
if we were to count by ten thousands,
the given number of 2,998,
would fall between zero and 10,000
and 5,000 would be right in the middle.
Now let's go ahead and plot
2,998 on the number line
which should be approximately here.
And now to round to the
nearest ten thousand,
we need to determine
whether the given number
is closer to zero or closer to 10,000.
And we can see it's closer to zero
and therefore, 2,998
rounds down to zero
when rounding to the nearest ten thousand.
And now let's use the
formal rules to round
to the nearest ten thousand.
Step one, we are asked to find the digit
in the rounding place value
but notice how there is no digit
in the ten thousands place value.
So if that's the case, we
can always add a zero here
and notice how it doesn't
change the value of the number.
So this zero is in the
rounding place value.
Step two, we look at the digit
to the right of the rounding place value
which is the two in the
thousands place value.
Because we have a two here
which is less than five,
we round down.
To round down the digit in
the rounding place value
stays the same while digits
to the right become zero.
Well the digit in the
rounding place value is zero
so this stays zero while
digits to the right become zero
so we end up getting zero
followed by four zeros
which is still just zero.
So here's another case
where using the number line
to round is very straight forward
but using the formal rules
can be a little tricky.
I hope you found this helpful.
