We're asked to complete the table to show each number rounded to the nearest ten
and the nearest hundred. And we'll show how to do this using the number line
as well as using the formal rules for rounding. So we first want to round five hundred eighty-four to the nearest
ten, so looking at this on the number line,
we need to recognize that five hundred eight-four is between five hundred eighty
and five hundred ninety to the nearest ten.
Then we'd have five hundred eighty-five in the middle.
Then notice that five hundred eighty-four would be here.
So notice to the nearest ten,
five hundred eighty-four is closer to five hundred eighty
than it is to five hundred ninety. Which is the reason why
five hundred eighty-four rounds down to five hundred eighty
to the nearest tens. Using our formal rules for rounding,
we first identify the digit in the ten place value, which is the eight.
The digit to the right determines whether we round up or down.
If it's a four or less you round down, five or more, round up.
So because it's a four we round down, meaning we keep the
eight the same and change the four to a zero,
giving us five hundred eighty. So we round down
the digit in the round off place value does not change.
Now we want to round five hundred eighty-four to the nearest hundred.
To the nearest hundred, five hundred eighty-four is between
five hundred and six hundred. Well we have five hundred fifty here in the middle.
Five hundred eighty-four would be approximately here.
Notice to the nearest hundred,
five hundred eighty-four is closer to six hundred than it is to five hundred.
So five hundred eighty-four rounds up to six hundred when rounding to the hundreds.
Using our formal rules,
we identified the digit in the hundreds place value, which is the five.
The digit to the right determines whether we round up or down.
So because we have an eight here, which is five or more we round up.
Because we're rounding up, we increase the five by one,
so it becomes six in the tens and the ones place value becomes zero,
giving us six hundred. Next we want to round
nine hundred seven to the tens and the hundreds. So nine hundred seven is between
nine hundred and nine hundred ten to the nearest ten,
where nine hundred five would be here in the middle. Notice nine hundred seven would be approximately here.
So because nine hundred seven is closer to nine hundred ten,
than it is to nine hundred to the nearest ten, nine hundred seven rounds up to nine hundred ten
when rounding to the tens place value. Using our formal rules,
notice how the zero was in the tens place value. The digit to the right,
the seven, because it's five or more indicates we round
up so we increase the zero to one,
and then ones place value changes to zero giving us nine hundred ten.
And now we want to round nine hundred seven to the nearest
hundreds. Nine hundred seven is between
nine hundred and one thousand to the nearest hundred.
Nine hundred fifty would be here in the middle.
Nine hundred seven is his way over here on left.
Because nine hundred seven is closer to nine hundred than it is to one thousand,
nine hundred seven rounds down to nine hundred
when rounding to the hundreds place value. Again using
the formal rules, the nine is in the hundreds place value,
the zero to the right indicates we round down,
so we don't change the nine and the tens and ones place value
changes to zero, because we're rounding to the hundreds.
And finally for our last example, we have ninety-eight.
So to the nearest ten,
ninety-eight is between ninety and one hundred. Ninety-five would be in the middle,
and ninety-eight would be approximately here.
Ninety-eight is closer to one hundred than it is to ninety,
and therefore, ninety-eight rounds up to one hundred when rounding to the tens place value.
And now rounding to the hundreds, ninety-eight is between zero and one hundred
to the nearest hundreds place value. So we'd have
zero here and
one hundred here. Fifty is in the middle and ninety-eight is over here on the far right,
very close to one hundred, which is the reason why to the nearest hundred,
ninety-eight rounds up to one hundred. Using our formal rules,
notice how we don't have a digit in the hundreds place value,
so if we had to include one it would be a zero. So the
zero is in the hundreds place value. The nine
indicates that we round up, because it's five or more, which means we increase the zero
by one
and replace the tens and ones place value with zeros,
giving us one hundred. The last thing I do want to mention is when rounding
using the number line, if the value happens to be right in the middle,
we always round up. That's the reason why using the formal rules
if the digit to the right is a five, we also round up.
I hope you found this helpful.