[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.50,0:00:02.52,Default,,0000,0000,0000,,Throughout your\Nmathematical life,
Dialogue: 0,0:00:02.52,0:00:06.03,Default,,0000,0000,0000,,you will find situations where\Nyou will need to round numbers.
Dialogue: 0,0:00:06.03,0:00:07.45,Default,,0000,0000,0000,,And you might be\Nsaying, well why?
Dialogue: 0,0:00:07.45,0:00:09.09,Default,,0000,0000,0000,,What situations might that be?
Dialogue: 0,0:00:09.09,0:00:10.66,Default,,0000,0000,0000,,Well, these would\Nbe situations where
Dialogue: 0,0:00:10.66,0:00:12.55,Default,,0000,0000,0000,,you're trying to get\Nan estimate on things.
Dialogue: 0,0:00:12.55,0:00:14.76,Default,,0000,0000,0000,,Where you're trying to--\Nmaybe you have a measurement
Dialogue: 0,0:00:14.76,0:00:17.72,Default,,0000,0000,0000,,and you want it to be a little\Nbit less exact to simplify
Dialogue: 0,0:00:17.72,0:00:18.22,Default,,0000,0000,0000,,things.
Dialogue: 0,0:00:18.22,0:00:20.72,Default,,0000,0000,0000,,Or you don't trust how\Nexact the measurement is.
Dialogue: 0,0:00:20.72,0:00:23.26,Default,,0000,0000,0000,,So here we're going to actually\Nthink about what rounding is.
Dialogue: 0,0:00:23.26,0:00:27.68,Default,,0000,0000,0000,,And we're going to round each of\Nthese numbers, 36, 34, 35, 26,
Dialogue: 0,0:00:27.68,0:00:28.55,Default,,0000,0000,0000,,and 12.
Dialogue: 0,0:00:28.55,0:00:31.65,Default,,0000,0000,0000,,We're going to round each\Nof them to the nearest 10.
Dialogue: 0,0:00:31.65,0:00:33.75,Default,,0000,0000,0000,,And I'll give you a\Nhint of what that means.
Dialogue: 0,0:00:33.75,0:00:36.08,Default,,0000,0000,0000,,That essentially says take\Neach of these numbers,
Dialogue: 0,0:00:36.08,0:00:39.94,Default,,0000,0000,0000,,and find the multiple of\N10 that it is closest to.
Dialogue: 0,0:00:39.94,0:00:41.30,Default,,0000,0000,0000,,So what are multiples of 10?
Dialogue: 0,0:00:41.30,0:00:43.75,Default,,0000,0000,0000,,Well, 10 times 0\Nis 0, 10 times 1
Dialogue: 0,0:00:43.75,0:00:48.70,Default,,0000,0000,0000,,is 10, 20, 30, 40, 50,\N60, so on and so forth.
Dialogue: 0,0:00:48.70,0:00:50.32,Default,,0000,0000,0000,,So I encourage you\Nto pause this video,
Dialogue: 0,0:00:50.32,0:00:52.30,Default,,0000,0000,0000,,and just based on what I just\Ntold you, what is the nearest
Dialogue: 0,0:00:52.30,0:00:54.13,Default,,0000,0000,0000,,multiple of 10 to\Neach of these numbers?
Dialogue: 0,0:00:54.13,0:00:56.30,Default,,0000,0000,0000,,Try to think about that.
Dialogue: 0,0:00:56.30,0:00:58.38,Default,,0000,0000,0000,,Well, to think about it a\Nlittle bit deeper, let's
Dialogue: 0,0:00:58.38,0:01:00.55,Default,,0000,0000,0000,,actually put a number line here.
Dialogue: 0,0:01:00.55,0:01:02.59,Default,,0000,0000,0000,,I'll put two number\Nlines over here.
Dialogue: 0,0:01:02.59,0:01:05.05,Default,,0000,0000,0000,,So we've got some\Nnumber lines here.
Dialogue: 0,0:01:05.05,0:01:06.94,Default,,0000,0000,0000,,And let's think about\Nwhere these points
Dialogue: 0,0:01:06.94,0:01:09.35,Default,,0000,0000,0000,,would sit on this number line.
Dialogue: 0,0:01:09.35,0:01:11.71,Default,,0000,0000,0000,,So this first number,\N36, where does it
Dialogue: 0,0:01:11.71,0:01:13.41,Default,,0000,0000,0000,,sit on this number line?
Dialogue: 0,0:01:13.41,0:01:15.36,Default,,0000,0000,0000,,Well, it's between 30 and 40.
Dialogue: 0,0:01:15.36,0:01:18.18,Default,,0000,0000,0000,,And this little blue mark\Nis 35, it's halfway between.
Dialogue: 0,0:01:18.18,0:01:21.44,Default,,0000,0000,0000,,So 36 is going to be a\Nlittle higher than that.
Dialogue: 0,0:01:21.44,0:01:25.49,Default,,0000,0000,0000,,So 36 is going to\Nbe right over here.
Dialogue: 0,0:01:25.49,0:01:28.43,Default,,0000,0000,0000,,And if we zoom in\Nbetween 30 and 40.
Dialogue: 0,0:01:28.43,0:01:33.17,Default,,0000,0000,0000,,So if we say that this\Nis 30, and this is 40,
Dialogue: 0,0:01:33.17,0:01:34.65,Default,,0000,0000,0000,,where is 36 going to be?
Dialogue: 0,0:01:34.65,0:01:36.11,Default,,0000,0000,0000,,So once again, this is 35.
Dialogue: 0,0:01:36.11,0:01:37.87,Default,,0000,0000,0000,,36 is one notch above that.
Dialogue: 0,0:01:37.87,0:01:41.70,Default,,0000,0000,0000,,So 36 is going to\Nbe right over here.
Dialogue: 0,0:01:41.70,0:01:45.19,Default,,0000,0000,0000,,So if we want to round to the\Nnearest 10, to the nearest
Dialogue: 0,0:01:45.19,0:01:48.74,Default,,0000,0000,0000,,multiple of 10, what are\Nthe two possibilities here?
Dialogue: 0,0:01:48.74,0:01:54.23,Default,,0000,0000,0000,,Well, I could take 36\Nand I could round up
Dialogue: 0,0:01:54.23,0:01:58.00,Default,,0000,0000,0000,,to the multiple of 10\Nabove it, which is 40.
Dialogue: 0,0:01:58.00,0:02:02.10,Default,,0000,0000,0000,,So I could round up to\N40, or I could round down
Dialogue: 0,0:02:02.10,0:02:08.16,Default,,0000,0000,0000,,to the multiple of 10\Nbelow it, which is 30.
Dialogue: 0,0:02:08.16,0:02:10.28,Default,,0000,0000,0000,,And so I need to figure\Nout which of these numbers
Dialogue: 0,0:02:10.28,0:02:11.60,Default,,0000,0000,0000,,is it closer to.
Dialogue: 0,0:02:11.60,0:02:14.34,Default,,0000,0000,0000,,Well, when you just look at\Nthat, even just eyeballing it,
Dialogue: 0,0:02:14.34,0:02:14.96,Default,,0000,0000,0000,,you can see it.
Dialogue: 0,0:02:14.96,0:02:17.83,Default,,0000,0000,0000,,But you could also say 36\Nis only four away from 40,
Dialogue: 0,0:02:17.83,0:02:20.67,Default,,0000,0000,0000,,and it's six away from\N30, it's closer to 40.
Dialogue: 0,0:02:20.67,0:02:22.82,Default,,0000,0000,0000,,So we are going to round up.
Dialogue: 0,0:02:22.82,0:02:25.24,Default,,0000,0000,0000,,We are going to round up to 40.
Dialogue: 0,0:02:25.24,0:02:27.46,Default,,0000,0000,0000,,This is literally\Ncalled rounding up.
Dialogue: 0,0:02:27.46,0:02:29.54,Default,,0000,0000,0000,,Now let's try some of\Nthese other numbers.
Dialogue: 0,0:02:29.54,0:02:31.97,Default,,0000,0000,0000,,What about 34?
Dialogue: 0,0:02:31.97,0:02:34.13,Default,,0000,0000,0000,,And I encourage you\Nto pause the video.
Dialogue: 0,0:02:34.13,0:02:35.50,Default,,0000,0000,0000,,Think about what\Nnumber you would
Dialogue: 0,0:02:35.50,0:02:38.04,Default,,0000,0000,0000,,get if you were to try to\Nround it up or round it down,
Dialogue: 0,0:02:38.04,0:02:40.97,Default,,0000,0000,0000,,and then which one it\Nis actually closer to.
Dialogue: 0,0:02:40.97,0:02:46.95,Default,,0000,0000,0000,,Well, 34 is right over\Nhere on this number line,
Dialogue: 0,0:02:46.95,0:02:52.22,Default,,0000,0000,0000,,where we zoom in, 34\Nis right over here.
Dialogue: 0,0:02:52.22,0:02:54.17,Default,,0000,0000,0000,,And we have two options.
Dialogue: 0,0:02:54.17,0:02:57.06,Default,,0000,0000,0000,,The multiple of\N10 above 34-- let
Dialogue: 0,0:02:57.06,0:03:02.92,Default,,0000,0000,0000,,me do those same colors-- the\Nmultiple of 10 above 34 is 40.
Dialogue: 0,0:03:02.92,0:03:06.81,Default,,0000,0000,0000,,Multiple of 10 below\N34, again, is 30.
Dialogue: 0,0:03:06.81,0:03:08.10,Default,,0000,0000,0000,,Now, which one is it closer to?
Dialogue: 0,0:03:08.10,0:03:10.78,Default,,0000,0000,0000,,Well it's only four away from\N30, and six away from 40,
Dialogue: 0,0:03:10.78,0:03:12.75,Default,,0000,0000,0000,,so it's closer to 30.
Dialogue: 0,0:03:12.75,0:03:15.70,Default,,0000,0000,0000,,So we are going to\Nround down to 30.
Dialogue: 0,0:03:19.75,0:03:21.28,Default,,0000,0000,0000,,And notice we went to 30.
Dialogue: 0,0:03:21.28,0:03:22.86,Default,,0000,0000,0000,,You might say, hey,\Nwhen we rounded it
Dialogue: 0,0:03:22.86,0:03:26.28,Default,,0000,0000,0000,,up the 10's place increased\Nfrom 3 to 4, from 30 to 40.
Dialogue: 0,0:03:26.28,0:03:28.02,Default,,0000,0000,0000,,Maybe when we round\Ndown, the 10's place
Dialogue: 0,0:03:28.02,0:03:30.97,Default,,0000,0000,0000,,will decrease from\N30 to 20, but no, 30
Dialogue: 0,0:03:30.97,0:03:33.21,Default,,0000,0000,0000,,is the multiple of 10 below 34.
Dialogue: 0,0:03:33.21,0:03:35.46,Default,,0000,0000,0000,,So when you round\Ndown, you just go--
Dialogue: 0,0:03:35.46,0:03:40.06,Default,,0000,0000,0000,,you keep the multiple of 10,\Nbut the ones place becomes a 0.
Dialogue: 0,0:03:40.06,0:03:42.22,Default,,0000,0000,0000,,Now let's try a really\Ninteresting one.
Dialogue: 0,0:03:42.22,0:03:48.16,Default,,0000,0000,0000,,Let's think about rounding the\Nnumber 35 to the nearest 10.
Dialogue: 0,0:03:48.16,0:03:49.79,Default,,0000,0000,0000,,And first, before we\Neven try to do it,
Dialogue: 0,0:03:49.79,0:03:51.09,Default,,0000,0000,0000,,let's think about\Nthe two options.
Dialogue: 0,0:03:51.09,0:03:52.26,Default,,0000,0000,0000,,Well, we've already seen it.
Dialogue: 0,0:03:52.26,0:03:54.45,Default,,0000,0000,0000,,35 is sitting right over here.
Dialogue: 0,0:03:54.45,0:03:57.76,Default,,0000,0000,0000,,On this number line, that\Nis 35, and once again we
Dialogue: 0,0:03:57.76,0:03:59.20,Default,,0000,0000,0000,,have two options.
Dialogue: 0,0:03:59.20,0:04:07.27,Default,,0000,0000,0000,,35, we can round it up to 40,\Nor we could round it down to 30.
Dialogue: 0,0:04:07.27,0:04:10.43,Default,,0000,0000,0000,,And I encourage you to pause\Nthe video and think about this.
Dialogue: 0,0:04:10.43,0:04:12.60,Default,,0000,0000,0000,,Well this one is a\Nlittle bit of a conundrum
Dialogue: 0,0:04:12.60,0:04:14.79,Default,,0000,0000,0000,,because it's five away\Nfrom both elements.
Dialogue: 0,0:04:14.79,0:04:17.34,Default,,0000,0000,0000,,It's five away from 40,\Nand five away from 30.
Dialogue: 0,0:04:17.34,0:04:19.05,Default,,0000,0000,0000,,So the mathematical\Ncommunity has
Dialogue: 0,0:04:19.05,0:04:21.38,Default,,0000,0000,0000,,decided to define\Nwhat to do in the case
Dialogue: 0,0:04:21.38,0:04:23.71,Default,,0000,0000,0000,,where you have a 5\Nin the ones place.
Dialogue: 0,0:04:23.71,0:04:27.69,Default,,0000,0000,0000,,If you have five or more in the\Nones place, you will round up.
Dialogue: 0,0:04:27.69,0:04:28.73,Default,,0000,0000,0000,,This is just a rule.
Dialogue: 0,0:04:28.73,0:04:31.85,Default,,0000,0000,0000,,Five or more in the ones\Nplace, you round up.
Dialogue: 0,0:04:31.85,0:04:35.45,Default,,0000,0000,0000,,So 35, you round up to 40.
Dialogue: 0,0:04:35.45,0:04:39.94,Default,,0000,0000,0000,,Notice, a 6 in the ones\Nplace was five or more.
Dialogue: 0,0:04:39.94,0:04:43.32,Default,,0000,0000,0000,,So if you're rounding to the\Nnearest 10, you round up to 40.
Dialogue: 0,0:04:43.32,0:04:49.09,Default,,0000,0000,0000,,A 4 in the ones place is not 5\Nor greater, so we rounded down.
Dialogue: 0,0:04:49.09,0:04:50.59,Default,,0000,0000,0000,,And so this gives\Na pretty good clue
Dialogue: 0,0:04:50.59,0:04:52.12,Default,,0000,0000,0000,,for these other two numbers.
Dialogue: 0,0:04:52.12,0:04:56.23,Default,,0000,0000,0000,,Let's try-- let's see\Nwhat happens with 26.
Dialogue: 0,0:04:56.23,0:04:58.35,Default,,0000,0000,0000,,26, what are the two options?
Dialogue: 0,0:04:58.35,0:05:00.37,Default,,0000,0000,0000,,What is a multiple\Nof 10 above 26,
Dialogue: 0,0:05:00.37,0:05:03.81,Default,,0000,0000,0000,,and what is a multiple\Nof 10 below 26.?
Dialogue: 0,0:05:03.81,0:05:08.46,Default,,0000,0000,0000,,Well, the multiple\Nof 10 above 26 is 30,
Dialogue: 0,0:05:08.46,0:05:12.40,Default,,0000,0000,0000,,and the multiple of\N10 below 26 is 20.
Dialogue: 0,0:05:12.40,0:05:14.03,Default,,0000,0000,0000,,So if we round up, we go to 30.
Dialogue: 0,0:05:14.03,0:05:17.29,Default,,0000,0000,0000,,If we round down, we go to 20.
Dialogue: 0,0:05:17.29,0:05:19.04,Default,,0000,0000,0000,,Well, if we're rounding\Nto the nearest 10,
Dialogue: 0,0:05:19.04,0:05:20.13,Default,,0000,0000,0000,,we look at the 10's place.
Dialogue: 0,0:05:20.13,0:05:20.98,Default,,0000,0000,0000,,That's what we're\Ngoing to round--
Dialogue: 0,0:05:20.98,0:05:22.89,Default,,0000,0000,0000,,we're going to round\Nto the nearest 10--
Dialogue: 0,0:05:22.89,0:05:24.50,Default,,0000,0000,0000,,but then we look\Nat the ones place.
Dialogue: 0,0:05:24.50,0:05:26.37,Default,,0000,0000,0000,,The ones place is\Ngoing to decide it.
Dialogue: 0,0:05:26.37,0:05:31.51,Default,,0000,0000,0000,,And we see here this\Nis 5 or greater.
Dialogue: 0,0:05:31.51,0:05:34.41,Default,,0000,0000,0000,,Or you could say this is\Ngreater than or equal to 5.
Dialogue: 0,0:05:34.41,0:05:36.46,Default,,0000,0000,0000,,So we round up.
Dialogue: 0,0:05:36.46,0:05:41.58,Default,,0000,0000,0000,,26 rounded to the nearest\N10, we round up to 30.
Dialogue: 0,0:05:41.58,0:05:44.06,Default,,0000,0000,0000,,Now what about 12?
Dialogue: 0,0:05:44.06,0:05:46.48,Default,,0000,0000,0000,,And I think you're\Ngetting the hang of this.
Dialogue: 0,0:05:46.48,0:05:49.75,Default,,0000,0000,0000,,Well let's think about the\Nmultiple of 10 above 12.
Dialogue: 0,0:05:49.75,0:05:51.81,Default,,0000,0000,0000,,So we could either\Nround up to 20.
Dialogue: 0,0:05:51.81,0:05:54.79,Default,,0000,0000,0000,,So 12 is sitting\Nright around here.
Dialogue: 0,0:05:54.79,0:05:59.23,Default,,0000,0000,0000,,We either round up to 20\Nor we round down to 10.
Dialogue: 0,0:05:59.23,0:06:01.43,Default,,0000,0000,0000,,Well, if we're going to\Nround to the nearest 10,
Dialogue: 0,0:06:01.43,0:06:03.59,Default,,0000,0000,0000,,we have to look\Nat the ones place.
Dialogue: 0,0:06:03.59,0:06:06.44,Default,,0000,0000,0000,,We have to look at the\Nones place right over here.
Dialogue: 0,0:06:06.44,0:06:09.09,Default,,0000,0000,0000,,This is less than 5.
Dialogue: 0,0:06:09.09,0:06:11.67,Default,,0000,0000,0000,,Since it's less than\Nfive, we round down,
Dialogue: 0,0:06:11.67,0:06:13.67,Default,,0000,0000,0000,,which makes sense because\Nit's also closer to 10
Dialogue: 0,0:06:13.67,0:06:15.02,Default,,0000,0000,0000,,than it is to 20.
Dialogue: 0,0:06:15.02,0:06:19.10,Default,,0000,0000,0000,,So we round down, and\Nrounding 12 to the nearest 10,
Dialogue: 0,0:06:19.10,0:06:21.61,Default,,0000,0000,0000,,you actually get 10.