Welcome to several
examples on how to round
whole numbers to the nearest hundred
or to the hundredths place value.
For each example, we'll
determine how to round the value
using the number line, as
well as how to use the formal
rules for rounding outlined here below.
In our first example,
we're asked to round 1938
to the nearest hundred.
So, using the number line, if
we were to count by hundreds,
notice how 1938 would fall
between 1900 and 2000.
And of course, 1950 would
be right in the middle.
So if we were to plot the
given value on the number line,
notice how it would be approximately here.
So to round 1938 to the
nearest hundred, we need to
determine whether the given
value is closer to 1900 or 2000.
And using the number line, we
can easily see the given value
is closer to 1900 and therefore
the given value rounds down
to 1900 when rounding
to the nearest hundred.
This number line technique always works,
but there is one special case.
If the given value happened
to fall right in the middle,
between the two possible rounded values,
the rule is we always round up.
Now let's round this again,
using the formal rules for rounding.
We begin with the given value.
Step one, we find or locate the digit
in the rounding place value,
which would be the nine,
in the hundredths place value.
And then we look at the digit to the right
of the rounding place value.
So the digit to the right
is a decision maker.
So in this case the three
in the tenths place value
is a decision maker.
If the digit to the
right is less than five,
we round down and because we have a three
to the right we do round down.
To round down, the digit
in the rounding place value
stays the same.
So the nine in the
hundredths stays the same,
while digits to the right become zero.
Notice how we have two
zeros to the right of the
nine in the hundredths
place value, giving us 1900.
If the digit to the right
happened to be five or more,
we round up.
In this case, we would have increased
the rounding place value
by one and all digits
to the right become zero.
Let's look at another example.
Here we're asked to round 5268
again to the nearest hundred.
So using the number line, if
we were to count by hundreds,
5268 would be between 5200 and 5300.
If we were to plot this
value on the number line,
because we know 5250 would
be right in the middle,
5268 would be, let's
say approximately here.
And because 5268 is closer
to 5300 than it is 5200,
the given value rounds
up to 5300 when rounding
to the nearest hundred.
Let's look at this again
using our formal rules.
So starting with the given value,
we first locate the digit
in the rounding place value.
Which is the two in the
hundredths and then we locate
the digit to the right,
which would be the six
in the tens place value.
So the six is a decision maker.
Because the digit to the right is a six,
which is five or more, we round up.
So to round up, the digit
in the rounding place value
increases by one.
So the two in the hundredths
increases by one, to three.
All digits to the right become zero.
So the tens and the ones
place value will become zero,
giving us 5300.
Let's look at two more examples
that are slightly different.
Here we're asked to round
42 to the nearest hundred.
So again, using the number line,
if we were to count by
hundredths, 42 would fall between
zero and 100 and of course, 50, again,
would be in the middle.
So if we were to plot
42 on the number line,
42 of course, is less than 50.
Let's say it's approximately here.
Because 42 is closer to
zero, than it is to 100,
when rounding to the nearest
hundred, 42 rounds to zero.
Using our formal rules for
rounding, if we begin with 42,
notice how we're asked to
find the digit in the rounding
place value, which is the
hundredths place value.
Notice how we don't have a digit
in the rounding place value,
but we could include a zero,
without changing the
value of the given number.
So, we have a zero in
the rounding place value.
And now we locate the digit to the right,
which would be the four
in the tens place value.
Because four is less
than five, we round down.
Which means the digit in
the rounding place value
stays the same.
So we keep a zero in the
hundredths place value,
while digits to the right become zero.
So we'd have zero followed
by two more zeros.
Well, zero zero zero, of
course, is still just zero.
So 42 rounds down to zero
when rounding to the hundreds.
For the next example,
we're asked to round 8050
to the nearest hundred.
So if we count by hundreds
on the number line,
8050 would be between 8000 and 8100.
And this is a special case
because notice how 8050
is actually right here in the middle,
meaning it's the same distance from 8000
as it is from 8100.
So in this special
case, we always round up
and we say that 8050 rounds up to 8100,
when rounding to the nearest hundred.
Using our formal rules for rounding,
beginning with the given
value we locate the digit
in the rounding place
value, which is the zero
in the hundredths.
Then we locate the digit to the right,
which is the five in the tens.
This is our decision maker.
So because this five is
five or more, we round up.
Which means the digit in
the rounding place value
increases by one.
So we increase the zero
in the hundreds to one
and all digits to the right become zero,
giving us 8100.
Next, we're asked to round
3975 to the nearest hundred.
If we count by hundreds, 3975 would fall
between 3900 and 4000.
If we were to plot the given
value on the number line,
it would be approximately here.
And because 3975 is closer
to 4000 than it is to 3900,
the given value rounds
up to 4000 when rounding
to the nearest hundred.
Using our formal rules,
starting with the given value.
We locate the digit in
the rounding place value,
which is the nine in the hundredths.
The digit to the right
is our decision maker,
which is the seven in
the tens place value.
And because seven is
five or more, round up.
So the digit in the rounding
place value increases by one.
All digits to the right become zero.
So this is a little bit
different because notice
how we have a nine in the hundredths.
So if we increase a nine by one we get 10.
And because 10 hundreds is equal to 1000,
we end up adding one to
the three in the thousands,
giving us a four in the thousands.
And all digits to the right become zero,
giving us 4000.
I hope you found these examples helpful.
Thank you for watching.
