0:00:00.500,0:00:02.520 Throughout your[br]mathematical life, 0:00:02.520,0:00:06.034 you will find situations where[br]you will need to round numbers. 0:00:06.034,0:00:07.450 And you might be[br]saying, well why? 0:00:07.450,0:00:09.090 What situations might that be? 0:00:09.090,0:00:10.660 Well, these would[br]be situations where 0:00:10.660,0:00:12.550 you're trying to get[br]an estimate on things. 0:00:12.550,0:00:14.758 Where you're trying to--[br]maybe you have a measurement 0:00:14.758,0:00:17.721 and you want it to be a little[br]bit less exact to simplify 0:00:17.721,0:00:18.220 things. 0:00:18.220,0:00:20.719 Or you don't trust how[br]exact the measurement is. 0:00:20.719,0:00:23.260 So here we're going to actually[br]think about what rounding is. 0:00:23.260,0:00:27.680 And we're going to round each of[br]these numbers, 36, 34, 35, 26, 0:00:27.680,0:00:28.550 and 12. 0:00:28.550,0:00:31.650 We're going to round each[br]of them to the nearest 10. 0:00:31.650,0:00:33.750 And I'll give you a[br]hint of what that means. 0:00:33.750,0:00:36.080 That essentially says take[br]each of these numbers, 0:00:36.080,0:00:39.940 and find the multiple of[br]10 that it is closest to. 0:00:39.940,0:00:41.300 So what are multiples of 10? 0:00:41.300,0:00:43.750 Well, 10 times 0[br]is 0, 10 times 1 0:00:43.750,0:00:48.695 is 10, 20, 30, 40, 50,[br]60, so on and so forth. 0:00:48.695,0:00:50.320 So I encourage you[br]to pause this video, 0:00:50.320,0:00:52.300 and just based on what I just[br]told you, what is the nearest 0:00:52.300,0:00:54.130 multiple of 10 to[br]each of these numbers? 0:00:54.130,0:00:56.297 Try to think about that. 0:00:56.297,0:00:58.380 Well, to think about it a[br]little bit deeper, let's 0:00:58.380,0:01:00.550 actually put a number line here. 0:01:00.550,0:01:02.590 I'll put two number[br]lines over here. 0:01:02.590,0:01:05.050 So we've got some[br]number lines here. 0:01:05.050,0:01:06.940 And let's think about[br]where these points 0:01:06.940,0:01:09.350 would sit on this number line. 0:01:09.350,0:01:11.710 So this first number,[br]36, where does it 0:01:11.710,0:01:13.410 sit on this number line? 0:01:13.410,0:01:15.360 Well, it's between 30 and 40. 0:01:15.360,0:01:18.180 And this little blue mark[br]is 35, it's halfway between. 0:01:18.180,0:01:21.440 So 36 is going to be a[br]little higher than that. 0:01:21.440,0:01:25.490 So 36 is going to[br]be right over here. 0:01:25.490,0:01:28.430 And if we zoom in[br]between 30 and 40. 0:01:28.430,0:01:33.170 So if we say that this[br]is 30, and this is 40, 0:01:33.170,0:01:34.650 where is 36 going to be? 0:01:34.650,0:01:36.110 So once again, this is 35. 0:01:36.110,0:01:37.870 36 is one notch above that. 0:01:37.870,0:01:41.700 So 36 is going to[br]be right over here. 0:01:41.700,0:01:45.190 So if we want to round to the[br]nearest 10, to the nearest 0:01:45.190,0:01:48.740 multiple of 10, what are[br]the two possibilities here? 0:01:48.740,0:01:54.230 Well, I could take 36[br]and I could round up 0:01:54.230,0:01:58.000 to the multiple of 10[br]above it, which is 40. 0:01:58.000,0:02:02.100 So I could round up to[br]40, or I could round down 0:02:02.100,0:02:08.160 to the multiple of 10[br]below it, which is 30. 0:02:08.160,0:02:10.280 And so I need to figure[br]out which of these numbers 0:02:10.280,0:02:11.600 is it closer to. 0:02:11.600,0:02:14.335 Well, when you just look at[br]that, even just eyeballing it, 0:02:14.335,0:02:14.960 you can see it. 0:02:14.960,0:02:17.830 But you could also say 36[br]is only four away from 40, 0:02:17.830,0:02:20.670 and it's six away from[br]30, it's closer to 40. 0:02:20.670,0:02:22.820 So we are going to round up. 0:02:22.820,0:02:25.240 We are going to round up to 40. 0:02:25.240,0:02:27.460 This is literally[br]called rounding up. 0:02:27.460,0:02:29.540 Now let's try some of[br]these other numbers. 0:02:29.540,0:02:31.970 What about 34? 0:02:31.970,0:02:34.126 And I encourage you[br]to pause the video. 0:02:34.126,0:02:35.500 Think about what[br]number you would 0:02:35.500,0:02:38.040 get if you were to try to[br]round it up or round it down, 0:02:38.040,0:02:40.970 and then which one it[br]is actually closer to. 0:02:40.970,0:02:46.950 Well, 34 is right over[br]here on this number line, 0:02:46.950,0:02:52.220 where we zoom in, 34[br]is right over here. 0:02:52.220,0:02:54.170 And we have two options. 0:02:54.170,0:02:57.060 The multiple of[br]10 above 34-- let 0:02:57.060,0:03:02.920 me do those same colors-- the[br]multiple of 10 above 34 is 40. 0:03:02.920,0:03:06.809 Multiple of 10 below[br]34, again, is 30. 0:03:06.809,0:03:08.100 Now, which one is it closer to? 0:03:08.100,0:03:10.780 Well it's only four away from[br]30, and six away from 40, 0:03:10.780,0:03:12.750 so it's closer to 30. 0:03:12.750,0:03:15.700 So we are going to[br]round down to 30. 0:03:19.750,0:03:21.280 And notice we went to 30. 0:03:21.280,0:03:22.863 You might say, hey,[br]when we rounded it 0:03:22.863,0:03:26.280 up the 10's place increased[br]from 3 to 4, from 30 to 40. 0:03:26.280,0:03:28.020 Maybe when we round[br]down, the 10's place 0:03:28.020,0:03:30.970 will decrease from[br]30 to 20, but no, 30 0:03:30.970,0:03:33.210 is the multiple of 10 below 34. 0:03:33.210,0:03:35.460 So when you round[br]down, you just go-- 0:03:35.460,0:03:40.060 you keep the multiple of 10,[br]but the ones place becomes a 0. 0:03:40.060,0:03:42.220 Now let's try a really[br]interesting one. 0:03:42.220,0:03:48.165 Let's think about rounding the[br]number 35 to the nearest 10. 0:03:48.165,0:03:49.790 And first, before we[br]even try to do it, 0:03:49.790,0:03:51.090 let's think about[br]the two options. 0:03:51.090,0:03:52.256 Well, we've already seen it. 0:03:52.256,0:03:54.450 35 is sitting right over here. 0:03:54.450,0:03:57.760 On this number line, that[br]is 35, and once again we 0:03:57.760,0:03:59.200 have two options. 0:03:59.200,0:04:07.270 35, we can round it up to 40,[br]or we could round it down to 30. 0:04:07.270,0:04:10.430 And I encourage you to pause[br]the video and think about this. 0:04:10.430,0:04:12.600 Well this one is a[br]little bit of a conundrum 0:04:12.600,0:04:14.790 because it's five away[br]from both elements. 0:04:14.790,0:04:17.339 It's five away from 40,[br]and five away from 30. 0:04:17.339,0:04:19.050 So the mathematical[br]community has 0:04:19.050,0:04:21.380 decided to define[br]what to do in the case 0:04:21.380,0:04:23.710 where you have a 5[br]in the ones place. 0:04:23.710,0:04:27.690 If you have five or more in the[br]ones place, you will round up. 0:04:27.690,0:04:28.730 This is just a rule. 0:04:28.730,0:04:31.850 Five or more in the ones[br]place, you round up. 0:04:31.850,0:04:35.450 So 35, you round up to 40. 0:04:35.450,0:04:39.940 Notice, a 6 in the ones[br]place was five or more. 0:04:39.940,0:04:43.320 So if you're rounding to the[br]nearest 10, you round up to 40. 0:04:43.320,0:04:49.091 A 4 in the ones place is not 5[br]or greater, so we rounded down. 0:04:49.091,0:04:50.590 And so this gives[br]a pretty good clue 0:04:50.590,0:04:52.120 for these other two numbers. 0:04:52.120,0:04:56.230 Let's try-- let's see[br]what happens with 26. 0:04:56.230,0:04:58.350 26, what are the two options? 0:04:58.350,0:05:00.370 What is a multiple[br]of 10 above 26, 0:05:00.370,0:05:03.810 and what is a multiple[br]of 10 below 26.? 0:05:03.810,0:05:08.460 Well, the multiple[br]of 10 above 26 is 30, 0:05:08.460,0:05:12.400 and the multiple of[br]10 below 26 is 20. 0:05:12.400,0:05:14.030 So if we round up, we go to 30. 0:05:14.030,0:05:17.290 If we round down, we go to 20. 0:05:17.290,0:05:19.040 Well, if we're rounding[br]to the nearest 10, 0:05:19.040,0:05:20.130 we look at the 10's place. 0:05:20.130,0:05:20.980 That's what we're[br]going to round-- 0:05:20.980,0:05:22.890 we're going to round[br]to the nearest 10-- 0:05:22.890,0:05:24.500 but then we look[br]at the ones place. 0:05:24.500,0:05:26.370 The ones place is[br]going to decide it. 0:05:26.370,0:05:31.510 And we see here this[br]is 5 or greater. 0:05:31.510,0:05:34.410 Or you could say this is[br]greater than or equal to 5. 0:05:34.410,0:05:36.460 So we round up. 0:05:36.460,0:05:41.580 26 rounded to the nearest[br]10, we round up to 30. 0:05:41.580,0:05:44.060 Now what about 12? 0:05:44.060,0:05:46.480 And I think you're[br]getting the hang of this. 0:05:46.480,0:05:49.750 Well let's think about the[br]multiple of 10 above 12. 0:05:49.750,0:05:51.810 So we could either[br]round up to 20. 0:05:51.810,0:05:54.790 So 12 is sitting[br]right around here. 0:05:54.790,0:05:59.230 We either round up to 20[br]or we round down to 10. 0:05:59.230,0:06:01.430 Well, if we're going to[br]round to the nearest 10, 0:06:01.430,0:06:03.590 we have to look[br]at the ones place. 0:06:03.590,0:06:06.440 We have to look at the[br]ones place right over here. 0:06:06.440,0:06:09.090 This is less than 5. 0:06:09.090,0:06:11.670 Since it's less than[br]five, we round down, 0:06:11.670,0:06:13.670 which makes sense because[br]it's also closer to 10 0:06:13.670,0:06:15.020 than it is to 20. 0:06:15.020,0:06:19.100 So we round down, and[br]rounding 12 to the nearest 10, 0:06:19.100,0:06:21.610 you actually get 10.