We're asked to round each decimal
to the indicated place value.
In the first example, we are given 3.8726
and asked to round to the hundredths.
Notice the given decimal has a seven
in the hundredths place value.
To the right of the hundredths
place value, we have a two.
Before we look at the formal
rules for rounding decimals,
let's use the number
line to round the decimal
to have a better understanding
of what it means to round.
To the hundredths place value,
notice how the given decimal
is between 3.87 and 3.88.
Let's show these values on
the number line to the right.
We would have 3.87 here
and 3.88 on the right.
By rounding 3.8726 to the
hundredths place value,
we are really determining
is the given decimal
closer to 3.87 or 3.88?
To help us locate the
location of the given decimal
in the number line,
notice how right in the
middle of these two decimals,
we would have 3.875
which means the given decimal 3.8726
is going to be between 3.87 and 3.875,
almost right in the middle,
let's say approximately here.
Notice how the given
decimal is closer to 3.87
than it is to 3.88 which
is why the given decimal
rounds to 3.87 when rounding
to the hundredths place value.
In this case, we would
say the given decimal
rounds down to 3.87.
Now, let's look at the formal
rules for rounding decimals.
Number one, we identify
the round-off place digit
which is the seven in the
hundredths place value
and the two to the right
is a decision maker.
If the digit to the right
of the round-off place digit
is less than five,
we do not change the
round-off place digit.
If it's five or more, we increase
the round-off place digit.
So because two is less than
five, we do not change the seven
and then in either case
we drop all digits to the right
of the round-off place digit
meaning we drop the two and the
six which does give us 3.87.
For the next example, we're
asked to round the given decimal
to the thousandths place value.
Notice we have a five in
the thousandths place value.
To the right of the five, we have a six.
Use the number line to the
thousandths place value
of the given decimal is
between 6.245 and 6.246.
Let's go ahead and label
those on the number line.
We have 6.245 and 6.246.
By rounding the given decimal
to the thousandths place value,
we are really determining
if the given decimal
is closer to 6.245 or 6.246.
To help us find the location
of the given decimal
in the number line,
right in the middle we would have 6.2455
and because our decimal is 6.2456,
it's going to be to the right of 6.2455,
let's say approximately here.
Because the given decimal
is closer to 6.246
than it is to 6.245,
the given decimal rounds up to 6.246.
Looking at the formal rules,
we identify the round-off
place digit which is the five.
The digit to the right is a six.
Because we have a six
which is five or more,
we increase the round-off
place digit by one
meaning we change this five to a six
and then in step three,
we drop the remaining digits to the right
which does give us 6.246.
For the last example,
we're asked to round 19.45
to the tenths place value.
Notice the given decimal has a four
in the tenths place value and
to the right we have a five.
The tenths place value, 19.45
is between 19.4 and 19.5.
Right in the middle, we would have 19.45
and notice the given decimal
is the decimal that's right in the middle
between 19.4 and 19.5.
Let's go ahead and label it.
Notice how the given
decimal is the same distance
from 19.4 as it is from 19.5.
So whenever the value
lies right in the middle,
the rule is to round up.
So we say 19.45 rounds up to 19.5.
Going back to the formal
rules one last time,
the four is the round-off place digit.
To the right, we have a five
and the rules say if the digit
to the right is five or more,
we increase the round-off
place digit by one
so we change the four to a five
and in step three, we drop
all digits to the right
of the round-off place digit.
So we drop the five in the
hundredths giving us 19.5.
I hope you found this helpful.
