### Video Transcript

What is the smallest whole number
that when rounded to the nearest hundred gives a result of 95,200?

Often when we’re asked a question
about rounding numbers, we’re given a number and asked to round it up. But in this question, we need to
think backwards. We’re given the answer, the rounded
number, but we need to find the smallest whole number that will round to this number
when we round it to the nearest hundred.

To begin with then, let’s think
about the rounded number that we have. 95,200 is made up of nine lots of
10,000, five 1,000s, and two 100s. Now, as we’ve said already, this is
the number after another number has been rounded to the nearest hundred. So to begin with, we need to think
about our hundreds digit. It’s been rounded to a two. But what could it have been?

Well, there’s only two possible
answers to that question. It could’ve been a one, and our
starting number could be ninety-five thousand one hundred and something, in which
case our number would’ve been rounded up to 95,200. Or the hundreds digit could be a
two, ninety-five thousand two hundred and something, in which case we’d be rounding
down to 95,200. But let’s not forget we’re looking
for the smallest whole number. The hundreds digit we’re looking
for then is one. But how many tens should our number
have?

Do you remember the rule about
digits for rounding? If a digit is four or less, we
round down. And if a digit is five or more, we
round up. If our tens digit was a nine, for
example, our number would be ninety-five thousand one hundred and ninety
something. This would round to 95,200. But we can go smaller than the nine
in the tens place because an eight would round up too, and a seven, a six, and we
can go one lower because we know if a digit is five or more, we round up. So the lowest possible tens digit
is five. Ninety-five thousand one hundred
fifty something is definitely going to round up to 95,200. It doesn’t matter what the ones
digit is. It’s still going to round to the
number we want.

But wait a moment! It does matter what the ones digit
is because we’re looking for the smallest whole number. There’s no point putting the digit
nine in there. We could go lower than that. We need to put the smallest
possible value digit, which is a zero, 95,150. Now, we know that 95,150 is
actually exactly halfway between 95,100 and 95,200. But with rounding, when we’re
looking at a number exactly at the halfway point, we always round up. We’ve looked at the value of each
digit in a five-digit number and used this to help us think about rounding. The smallest whole number that if
we rounded to the nearest hundred will give us a result of 95,200 is the number
95,150.