Welcome to a lesson that will show
how to round 7,345,862 to various place values,
using both a number line, as well as the
formal rules for rounding outlined below.
In our first example, we're asked to round 7,345,862
to the nearest million; so to round this using the
number line, if we were to count by millions, notice how
the given number would be between seven million
and eight million, where in the middle,
we would have 7,500,000.
And now let's go ahead and plot 7,345,862 on this number
line, we know it's less than 7,500,000, so let's just say
it's approximately here, to round this number to the nearest
million, we need to determine whether this number is
closer to seven million or closer to eight million.
And notice how because the given number is closer to
seven million, the given number rounds down to seven
million, when rounding to the millions place value.
The method of rounding using the number line always works,
but there is one special case; if the given number happens
to be right in the middle, between the two possible
rounding values, the rule is we always round up.
Now let's round the given number to the nearest million
using the formal rules for rounding.
Step one, we find the digit in the rounding place value,
because we're rounding to the nearest million, notice
how the seven is in the millions place value; step two,
we look at the digit to the right of the rounding place
value, which in this case is the three, in the
hundred-thousands place value; so the three's our
decision maker, it tells us to round up or down.
So because we have a three, and a three is less than five,
we round down; to round down, the digit in the rounding
place value stays the same, all digits to the right become
zero, because we're rounding down, the seven in the millions
place value stays seven, and all digits to the
right become zero, giving us seven million.
If the three happened to be five or more, we would round up,
which means the digit in the rounding place value increases
by one, and all digits to the right become zero.
Let's look at our next example.
We have the same number, but now we're rounding to the
nearest ten thousand, so using the number line, if we
were to count by ten thousands, notice how 7,345,862
would be between 7,340,000 and 7,350,000.
And again, it's helpful to find the value in the middle,
which in this case it'd be 7,345,000.
So notice how the given number is larger than 7,345,000,
so let's say it's approximately here, so because the given
number is closer to 7,350,000 than it is to 7,340,000,
the given number rounds up to 7,350,000.
Using our formal rules, step one, we find the digit
in the rounding place value, which in this case would be the
four, in the ten-thousands place value; step two, we look at
the digit to the right of the rounding place value, which
in this case is the five, in the one-thousands place value,
and because we have a five here, and five is five or more,
we round up, the digit in the rounding place value increases
by one, which means we increase the four in the
ten-thousands place value to a five,
and all digits to the right become zero.
So we have zero, zero, zero, zero,
which does give us 7,350,000.
Let's look at at least one more example.
We're asked to round the same number to the nearest
hundred-thousand this time, so using the number line,
if we were to count by hundred-thousands, 7,345,862 would
fall between 7,300,000 and 7,400,000, where once again
in the middle we would have 7,350,000.
So plotting this number on the number line, it's less
than this middle value, so let's just say it's approximately
here, so because it's to the left of the number in the
middle, we can easily see that the given number is closer
to 7,300,000 than it is to 7,400,000, and therefore the
given number rounds down to 7,300,000,
when rounding to the nearest hundred-thousand.
Using our formal rules one last time, we begin by locating
the digit in the rounding place value, which in this case
is the three in the hundred-thousands place value,
now we look at the digit on the right, which is the four
in the ten-thousands place value, so the four's our
decision maker, because four is less than five, we round
down, which means the digit in the rounding place value
stays the same, so the three stays the same, all digits
to the right become zero, giving us 7,300,000.
So it's important to notice, when rounding down, we do not
change the digit in the rounding place value, but when
rounding up, we do increase it by one.
I hope you found this helpful.