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

What is the smallest whole number that when rounded to the nearest thousand gives a result of 745000? [A] 745499 [B] 744999 [C] 744500 [D] 744999

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Video Transcript

What is the smallest whole number that when rounded to the nearest thousand gives a result of 745000? 745499, 744999, 744500, or 744999.

So out of the four possible answers, we’re looking for a number that rounds to 745000 when we round it to the nearest thousand. But we’re not just looking for any number that rounds to this amount. We’re looking for the smallest number, the smallest whole number. There are two possible ways that we could approach this problem.

The first is that we could go through each of the possible answers in turn. We could ask ourselves which of them rounds to 745000 when they’re rounded to the nearest thousand. And then, surely, the smallest of these answers will be the correct answer. But if we use this method, it doesn’t really teach us anything about what looking for the smallest whole numbers like. Instead, let’s use a different method.

Let’s think about the number that we need to round to and what sort of numbers will round to this number and then try to work out what the smallest whole number might be. And once we’ve done that, we can come back to our list and try to find that number, hopefully it’s there. So first of all, let’s think about where our number 745000 belongs on a number line. Well, the thousands either side of it are 744000 and 746000. And halfway between these multiples of a thousand are the five hundred numbers: 744500 and 745500. These halfway points are important because we often look at the halfway point when deciding whether to around a number up or down. So let’s think about all the numbers that we’re going to round to 745000.

All the numbers that are closest to 745000 are in this space. We need to look at the hundreds digit to decide whether we around a number up or down. If the hundreds digit is five or more, we round up and if it’s less than five, we round down. In the number 745500, we have five hundreds. So that number rounds up. We don’t round that to 745000. But if we look at the number one less than this, we have the number 745499. This number has four hundreds. And so, we round it down to 745000. But we can see that this is the greatest whole number that rounds to 745000. We need to look at the number at the other end of our scale.

What’s the smallest whole number that rounds up to 745000? When we’re quite close to our halfway point again, let’s start with that. 744500 has a five in the hundreds column. And so, we know that this definitely rounds up to 745000. Could this be the answer? Let’s think about the number one less than this: 744499. This number has a four in the hundreds column. So if we go one less than the halfway point, we need to round down to 744000. And so, we can see that the smallest whole number is actually the halfway point between 744000 and 745000. The answer is 744500. Is that one of the possible answers on our list? Yes, it is.

Interestingly, by using this method to find out the answer, we found out something about the first number on our list. It’s actually the largest whole number that when rounded to the nearest thousand gives a result of 745000. But of course, the question didn’t ask for the largest whole number. It asked for the smallest whole number.

The smallest whole number that when rounded to the nearest thousand gives a result of 745000 is 744500.

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