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Question Video: Finding the Smallest Whole Number That When Rounded to the Nearest Hundred Gives a Certain Result Mathematics

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

03:35

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.

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