let's look at the basics of digits and place value
you're definitely going to need to know these places
the ones digit
he's the furthest to the right in a whole number
we won't talk about decimals just yet
to the left of him
is the tens digit
then the hundreds
then the thousands now at this point you don't have to put a comma
but you can
now in the next one if you have a number
like ten thousand, out to the ten thousand, you're required to put a comma
that's the rule or i'll tell you right you'll get marked wrong
after ten thousands
is the hundred thousands digit
and then the millions digit
and so on
the ten millions digit and
so on
okay that's high enough for our purposes
now, suppose if you would that I asked you to round a number
((pay attention boys, I'll show you how it's done))
well, of course you're going to need to know to round to which digit
in this case we're going to ask you to round five hundred and sixty five to the nearest tens digit
you need to know where that is
there is the tens digit
so everything after that
is going to be a zero everything after
we have to ask ourselves
is our answer going to be five hundred and six and a zero
or five hundred and seven and a zero
what's going to help us to decide
is the next digit
this is a confusing part, the digit after
the tens, in this case the one you're rounding to
now if you think about that, that one digit after
SFX
in this case
that five, the ones digit
can only be
zero one two three four five six seven eight or nine, it can only be one of those ten
things tens not one of them is it? zero is
can only be one of those because you only get one symbol or one numeral
and it's kind of divided into two parts
the lower ones zero one two three or four
and the higher ones
five six seven eight or nine most people
think fives right in the middle but it really isn't, is it?
fives in the higher group
soooo
SFX
we see that the next digit is in the higher group, so that means we're gonna go up
and rounding five sixty five to the nearest ten, it equals five hundred and
seventy
let's do another one, let's round this number
to the nearest thousand
now you gotta pay attention to what your rounding to, first thing i do is find
that digit, the thousands
((SFX)) There it is, that means everything after that is going to be a zero
SFX
it's either going to be
two hundred and sixty seven thousand with all zeros or two hundred
and sixty eight thousand
now who's going to decide
the next digit
and the next digit is a three and that's going to be in the lower group isn't it?
so
in this case
we're gonna stay at the same number, it's gonna be; we never go down by the way,
it's going to be two hundred sixty seven thousand
let's just do one more in this case we want to round the same number to the nearest
gotta pay attention to the nearest
hundreds
and there is the hundreds digit you gotta make sure you know all your digits
so
it's either going to be
two hundred and sixty seven thousand three hundred
note a different answer 'cause we're rounding to a different digit
or two hundred and sixty seven thousand
four hundred
who's going to decide
then next digit
next digit changes depending on what your rounding too
in this case the next digit
is six
six is certainly in the upper half
or the higher numbers if you would more than half way
so your numbers two six seven
four hundred, two hundred and sixty seven thousand four hundred
got the idea
SFX
now we don't just round for the sake of rounding, we round to make things
easier
for instance
suppose i ask you to add these numbers up
now you could
but (SFX) it would be hard, it'd take you a long time. What if you only needed an estimate?
well i wouldn't add them up and then round cause I'd still have to go through the
trouble of adding them all up and that's still hard
what i would do (SFX)
i would round each number first, it would make life easier
now in this case
i'm going to round
to the nearest hundred, as they all have hundreds
and plus the directions told me to do that
two ninety four to the nearest hundred rounds to three hundred
six thirteen
rounds to
six hundred cause i said hundreds now
and one thousand six hundred seventy-one we're rounding to the nearest hundred now
so we're going to round to
seventeen hundred now this makes it way easier to add them up
because zeros are easy to deal with, you just add them up
and this estimated sum is
two thousand six hundred, way faster and easier
in fact
what's the real answer? If I add up the real answer i get two thousand five and
seventy eight which is
pretty close, now if you need to be exact then of course you need to be exact when you
go through the work but if you don't
you can use rounding to make
your problems easier
note that we rounded each number first
and then added
to make it easier, you don't add and go to all the trouble of a adding
and then round
okay you round first because it makes things easier
let's estimate a distance here
by rounding
now the distance from germantown to richmond
ninety four miles the distance from richmond to atlanta
is three hundred seventy nine miles and the distance from atlanta to miami
is two hundred eighty one miles. Now if I wanted to just get in estimate of how
far it is
from germantown to miami
i could add them all up, well i'd have to estimate first
and what i would do
ninety four
would round to, let's round
to the
hundreds
even though they didn't tell me i picked hundreds ok because it's the easiest i
could round it tens
but i think if you have your choice and they don't tell you, pick the higher one
now three hundred and seventy nine
is going to round to,
in hundreds now
closer to four hundred because of its seven
and two hundred eighty-one in hundreds
is going to round to
three hundred
now this is very easy we've made it easy 'cause we rounded
first
add up those three numbers
and it's about eight hundred miles from germantown to miami
it's important to know how to estimate
just remember that
ok let's do one more
finishing up your semester i see joe has these scores, fifty nine, seventy four
eighty nine and eighty five, on his math test. let's estimate the total
now since they all have tens
rather than add them all up
let's
get an approximate sum
by rounding, remember round first,
fifty nine rounds to sixty
seventy four rounds to seventy 'cause four
has to stay the same
eighty-nine goes up to ninety
and eighty-five, remember about five, five is not in the middle five is in the
upper group
that rounds to ninety, it's gonna be much easier to add them now
they add up to
three hundred and ten
okay? okay, go try the homework get busy.