WEBVTT 00:00:01.420 --> 00:00:10.910 What is the smallest whole number that when rounded to the nearest thousand gives a result of 745000? 00:00:12.390 --> 00:00:31.750 745499, 744999, 744500, or 744999. 00:00:33.570 --> 00:00:43.390 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. 00:00:44.280 --> 00:00:46.930 But we’re not just looking for any number that rounds to this amount. 00:00:47.040 --> 00:00:50.680 We’re looking for the smallest number, the smallest whole number. 00:00:51.650 --> 00:00:54.580 There are two possible ways that we could approach this problem. 00:00:55.210 --> 00:00:59.190 The first is that we could go through each of the possible answers in turn. 00:00:59.630 --> 00:01:07.140 We could ask ourselves which of them rounds to 745000 when they’re rounded to the nearest thousand. 00:01:07.850 --> 00:01:11.520 And then, surely, the smallest of these answers will be the correct answer. 00:01:12.810 --> 00:01:19.660 But if we use this method, it doesn’t really teach us anything about what looking for the smallest whole numbers like. 00:01:20.330 --> 00:01:22.900 Instead, let’s use a different method. 00:01:24.030 --> 00:01:35.190 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. 00:01:36.270 --> 00:01:40.640 And once we’ve done that, we can come back to our list and try to find that number, hopefully it’s there. 00:01:41.700 --> 00:01:47.590 So first of all, let’s think about where our number 745000 belongs on a number line. 00:01:48.470 --> 00:01:55.860 Well, the thousands either side of it are 744000 and 746000. 00:01:57.100 --> 00:02:08.000 And halfway between these multiples of a thousand are the five hundred numbers: 744500 and 745500. 00:02:08.240 --> 00:02:16.120 These halfway points are important because we often look at the halfway point when deciding whether to around a number up or down. 00:02:17.240 --> 00:02:22.770 So let’s think about all the numbers that we’re going to round to 745000. 00:02:23.670 --> 00:02:28.850 All the numbers that are closest to 745000 are in this space. 00:02:29.570 --> 00:02:34.050 We need to look at the hundreds digit to decide whether we around a number up or down. 00:02:34.720 --> 00:02:41.240 If the hundreds digit is five or more, we round up and if it’s less than five, we round down. 00:02:42.660 --> 00:02:48.690 In the number 745500, we have five hundreds. 00:02:49.250 --> 00:02:50.680 So that number rounds up. 00:02:50.940 --> 00:02:53.790 We don’t round that to 745000. 00:02:54.390 --> 00:03:01.830 But if we look at the number one less than this, we have the number 745499. 00:03:02.440 --> 00:03:04.450 This number has four hundreds. 00:03:05.050 --> 00:03:08.800 And so, we round it down to 745000. 00:03:09.730 --> 00:03:14.860 But we can see that this is the greatest whole number that rounds to 745000. 00:03:15.530 --> 00:03:18.680 We need to look at the number at the other end of our scale. 00:03:19.250 --> 00:03:25.950 What’s the smallest whole number that rounds up to 745000? 00:03:26.740 --> 00:03:30.810 When we’re quite close to our halfway point again, let’s start with that. 00:03:31.420 --> 00:03:38.060 744500 has a five in the hundreds column. 00:03:38.930 --> 00:03:43.660 And so, we know that this definitely rounds up to 745000. 00:03:44.600 --> 00:03:45.850 Could this be the answer? 00:03:47.140 --> 00:03:54.830 Let’s think about the number one less than this: 744499. 00:03:55.510 --> 00:03:57.840 This number has a four in the hundreds column. 00:03:58.580 --> 00:04:05.730 So if we go one less than the halfway point, we need to round down to 744000. 00:04:06.820 --> 00:04:14.130 And so, we can see that the smallest whole number is actually the halfway point between 744000 and 745000. 00:04:15.120 --> 00:04:19.080 The answer is 744500. 00:04:20.060 --> 00:04:22.300 Is that one of the possible answers on our list? 00:04:23.130 --> 00:04:24.220 Yes, it is. 00:04:25.630 --> 00:04:32.020 Interestingly, by using this method to find out the answer, we found out something about the first number on our list. 00:04:33.070 --> 00:04:40.240 It’s actually the largest whole number that when rounded to the nearest thousand gives a result of 745000. 00:04:41.110 --> 00:04:43.840 But of course, the question didn’t ask for the largest whole number. 00:04:43.840 --> 00:04:45.580 It asked for the smallest whole number. 00:04:46.410 --> 00:04:58.390 The smallest whole number that when rounded to the nearest thousand gives a result of 745000 is 744500.