We're asked to round 4,993
to the nearest thousand
as well as to the nearest hundred.
We'll be discussing how to
round using the number line
as well as the formal rules
for rounding, outlined below.
Let's first round 4,993
to the nearest thousand.
So using the number line, if
we were to count by thousands,
notice how 4,993 would fall
between 4,000 and 5,000.
So on the number line we
have a 4,000 on the left,
a 5,000 on the right.
In the middle we have 4,500.
Next we'll plot 4,993 on this number line.
Notice how it would be
here on the far right,
close to 5,000.
Now to use a number line to
round to the nearest thousand,
we need to determine whether
the given number is closer
to 5,000 or closer to 4,000.
And we can easily see
it's closer to 5,000,
which means 4,993 rounds up to 5,000
when rounding to the nearest thousand.
And let's also round the
given number using the
formal rules for rounding.
So beginning with the given number,
step one, we identify the digit
in the rounding place value.
Because we're rounding
to the nearest thousand,
the digit in the rounding
place value is the four
in the thousands place value.
Step two, we look at
the digit to the right
of the rounding place value,
which in our case is the nine
in the hundreds place value.
If the digit to the right is
less than five we round down.
If the digit is five or more, we round up.
So because the digit
to the right is a nine,
which is five or more, we round up.
To round up, the digit in
the rounding place value
increases by one and all digits
to the right become zero.
So we want to increase the four
in the thousands place value
by one, and therefore
it would have a five.
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, giving
us a rounded value of 5,000.
Now let's round the same
number to the nearest hundred.
So using the number
line, if we were to count
by hundreds now, 4,993 would fall between
4,900 and 5,000 and in the
middle we'd have 4,950.
Now we want to plot
4,993 on the number line,
which is going to be
to the right of 4,950,
let's just say approximately here.
Now to round to the nearest hundred,
we need to determine
whether the given number
is closer to 5,000 or closer to 4,900.
And once again we can
see it's closer to 5,000,
which means 4,993 rounds up to 5,000
when rounding to the nearest hundred.
So notice how in this case,
rounding the given number
to the nearest thousand
and the nearest hundred
results in the same rounded value.
Let's also round to the nearest hundred
using our formal rules.
So beginning with 4,993, step one,
we find the digit in the
rounding place value,
so we're looking for the digit
in the hundreds place value,
which is this nine here.
Step two, we look at the digit
to the right of the rounding place value,
which is the nine in the tens place value.
If the digit to the right
is less than five, we round down,
if it's five or more, we round up.
So because the digit to the right
is a nine, 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 increase the nine
in the hundreds by one,
which would give us ten hundreds,
so because we have ten hundreds,
which is equal to 1,000,
we perform an exchange and
we add a one to the four
in the thousands place value
so the four becomes a five.
All digits to the right become zero,
giving us a rounded value of 5,000.
It didn't occur in these two examples,
but if the digit to the right
of the rounding place value
is less than five, we round down.
To round down, the digit
in the rounding place value
stays the same and all digits
to the right become zero.
I hope you found this helpful.
