WEBVTT 00:00:01.580 --> 00:00:17.250 What is the largest nine-digit number that can be formed using all the digits of six, six, seven, nine, seven, five, zero, one, and three? 00:00:18.720 --> 00:00:21.640 As part of the question, we’re given nine digits. 00:00:21.640 --> 00:00:23.450 Those nine digits we’ve just read out. 00:00:24.250 --> 00:00:29.520 And we need to rearrange those digits so that they make the largest possible nine-digit number. 00:00:30.590 --> 00:00:34.490 Now, we know that the value of a digit in a number depends on where we write it. 00:00:35.110 --> 00:00:42.200 For example, the digit three might have a value of three tens or three thousands, maybe even three millions. 00:00:42.700 --> 00:00:44.820 It depends where we write it in the number. 00:00:45.620 --> 00:00:53.950 So, perhaps the first thing we should do is to draw a place value grid to think about what the value of each digit in a nine-digit number is going to be. 00:00:54.590 --> 00:00:57.330 We can think of our digits in groups of three. 00:00:58.090 --> 00:01:02.950 So, going from right to left, we could call our first group of three the ones. 00:01:03.630 --> 00:01:08.750 And we have the ones, tens, and hundreds digits. 00:01:09.820 --> 00:01:13.290 Our second group of three are our thousands. 00:01:13.750 --> 00:01:20.700 Here, we have the thousands digit, ten thousands digit, and hundred thousands digit. 00:01:22.010 --> 00:01:24.960 Our final group of three are our millions. 00:01:25.570 --> 00:01:31.450 We have the millions, tens of millions, and hundred millions digits. 00:01:32.380 --> 00:01:35.800 Let’s start by thinking about the hundred millions place. 00:01:36.600 --> 00:01:43.140 If we want to make a digit that’s the largest possible nine-digit number, which digit do we want to put in the hundred millions place? 00:01:43.230 --> 00:01:45.160 This is the place with the largest value. 00:01:45.160 --> 00:01:50.720 Well, there’s no point putting a one in there because there are other digits that are greater. 00:01:51.260 --> 00:01:54.430 We could even do better than a three or a five. 00:01:55.270 --> 00:02:01.500 Instead of just going through each digit, we can say to ourselves that we just need to pick the largest possible digit. 00:02:02.020 --> 00:02:06.490 And if we look at our list of digits, the largest possible digit is nine. 00:02:07.540 --> 00:02:11.770 So, the largest possible number will have nine hundred millions. 00:02:12.710 --> 00:02:16.800 It can sometimes be tricky to spot which digits we’ve used and which we haven’t. 00:02:17.170 --> 00:02:21.240 So, what we’ll do is we’ll write them out underneath and we’ll rub them out as we use each one. 00:02:21.840 --> 00:02:24.470 So, to begin with, we’ve used the digit nine. 00:02:25.730 --> 00:02:29.860 The next place with the greatest value is the ten millions place. 00:02:30.120 --> 00:02:35.830 And again, to make this number have the largest possible value, we need to pick the next largest digit. 00:02:36.260 --> 00:02:41.380 We’ve used the digit nine, so the digit with the next largest value is seven. 00:02:42.690 --> 00:02:44.690 So, let’s cross off seven from our list. 00:02:45.440 --> 00:02:49.490 And there’s another seven in our list, so we can put this in the millions place. 00:02:50.180 --> 00:02:55.030 What we’re doing really is putting the digits in order from largest to smallest. 00:02:55.600 --> 00:02:58.410 This is going to give us the largest possible nine-digit number. 00:02:59.210 --> 00:03:01.820 The next largest digits are two sixes. 00:03:02.120 --> 00:03:06.070 And we can put these in the hundred thousands and ten thousands places. 00:03:09.230 --> 00:03:12.400 In our thousands place, we need to put the digit five. 00:03:15.880 --> 00:03:18.620 And then, we’re left with a digit zero, one, and three. 00:03:18.650 --> 00:03:23.460 And if we put these in order from largest to smallest, we get 310. 00:03:26.130 --> 00:03:39.590 We’ve found the answer by rearranging the digits from largest to smallest so that the largest digit has the largest possible value and the smallest digit has the smallest possible value. 00:03:40.790 --> 00:03:54.950 So, the largest nine-digit number that we can make using the digits six, six, seven, nine, seven, five, zero, one, three is 977665310.