Here we are asked to round 282
to the nearest 10
and then also round 282
to the nearest 10,000.
We will be discussing how to round
using both the number line
as well as the formal rules for rounding
outlined below.
Let's begin by rounding
282 to the nearest 10
so using the number line
if you go to count by 10s,
we need to recognize that
282 would be between 280 and 290
and 285 would be in the middle.
So to round 282 to the nearest 10,
we now want to plot 282 on the number line
and see if it is closer to 280 or 290.
282 would be approximately here
and because 282 is closer to 280
than it is to 290,
282 rounds down to 280
when rounding to the nearest 10.
So this technique of rounding
using the number line
always works but there
is one special case.
If the given number happened to be
right in the middle,
between the two possible rounded values,
then we always round up.
Now let's also round this
using the formal rules for
rounding outlined below.
Beginning with 282
step one we find the digit
in the rounding place value
which because of rounding
to the nearest 10
would be eight in the 10's place value.
Step two we look at the digit
to the right of the rounding place value
which in this case is the two
and one's place value
and because two is less than five,
we round it down,
which means a digit in
the rounding place value
stays the same,
all digits to the right become zero
so the eight in the 10's place value
stays eight and the two
in the one's place value
because it is on the right becomes zero
giving us 280.
Now let's look at the second
part of this question,
which can be little tricky using the
formal rules of rounding.
Let's first round 282
to the nearest 10,000
using the number line.
So if you only count by 10,000s
we need to recognize that
the given number of 282,
would fall between zero and 10,000.
And again 5000 would be in the middle.
So now we plot 282 in the number line
by using this scale
would be fairly close to zero
let's just say approximately here
and because 282 is closer to zero
than it is to 10,000
when running to the nearest 10,000
282 rounds to zero.
So again using the number line
this is still straightforward
but also could be formal rules of rounding
to determine how to round
282 to the nearest 10,000.
So we begin with 282,
and notice how the first step
is to find the digit and
the rounding place value
which would be the digit in
the 10,000's place value.
Notice how we don't have
a 10,000s place value
what we could do
is add a zero in the 1000's place value
and a zero to the 10,000's place value.
Notice how this number is still at 282
and now we can identify the digit
in the rounding place value
which is this zero here
again in the 10,000's place value.
Step two we look at the digit to the right
of the running place value
which in this case is the zero
in the 1000's place value
because zero is less than five,
we round down
and again to round down
the digit and the rounding place value
stays the same
so this zero here stays zero
and the rule says all digits to the right
become zero
so we would have zero
followed by zero, zero, zero, zero
which of course is just zero.
So in this case the
formal rules of rounding
are a little bit trickier
than using the number line.
I hope you found this helpful.
