[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.11,Default,,0000,0000,0000,,Welcome to the presentation on ordering numbers.
Dialogue: 0,0:00:04.14,0:00:05.93,Default,,0000,0000,0000,,Lets get started with some problems that I think,
Dialogue: 0,0:00:05.94,0:00:08.24,Default,,0000,0000,0000,,as you go through the examples hopefully,
Dialogue: 0,0:00:08.29,0:00:10.17,Default,,0000,0000,0000,,you'll understand how to do these problems.
Dialogue: 0,0:00:10.22,0:00:11.66,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:00:11.69,0:00:14.17,Default,,0000,0000,0000,,The first set of numbers that we have to order \N
Dialogue: 0,0:00:14.20,0:00:44.14,Default,,0000,0000,0000,,is 35.7%,108.1%, 0.5, 13/93, and 1 and 7/68
Dialogue: 0,0:00:44.19,0:00:45.72,Default,,0000,0000,0000,,So let's do this problem.
Dialogue: 0,0:00:45.74,0:00:48.27,Default,,0000,0000,0000,,The important thing to remember whenever you're \N
Dialogue: 0,0:00:48.27,0:00:52.03,Default,,0000,0000,0000,,doing this type of ordering of numbers is to realize
Dialogue: 0,0:00:52.03,0:00:54.99,Default,,0000,0000,0000,,that these are all just different ways to represent
Dialogue: 0,0:00:55.05,0:00:58.74,Default,,0000,0000,0000,,these are all a precent or a decimal or a fraction or
Dialogue: 0,0:00:58.75,0:01:02.08,Default,,0000,0000,0000,,a mixed number--are all just different \Nways of representing numbers.
Dialogue: 0,0:01:02.12,0:01:04.87,Default,,0000,0000,0000,,It's very hard to compare when \Nyou just look at it like this,
Dialogue: 0,0:01:04.90,0:01:07.47,Default,,0000,0000,0000,,so what I like to do is I like to \Nconvert them all to decimals.\N
Dialogue: 0,0:01:07.49,0:01:11.67,Default,,0000,0000,0000,,But, you know,there could be someone who \Nlikes to convert them all to percentages
Dialogue: 0,0:01:11.67,0:01:13.94,Default,,0000,0000,0000,,or convert them all to fractions and then compare.
Dialogue: 0,0:01:14.01,0:01:16.60,Default,,0000,0000,0000,,But I always find decimals to be \Nthe easiest way to compare.
Dialogue: 0,0:01:16.60,0:01:19.30,Default,,0000,0000,0000,,So let's start with this 35.7%.\N
Dialogue: 0,0:01:19.30,0:01:21.53,Default,,0000,0000,0000,,Let's turn this into a decimal.
Dialogue: 0,0:01:21.59,0:01:25.44,Default,,0000,0000,0000,,Well, the easiest thing to remember is\Nif you have a percent
Dialogue: 0,0:01:25.44,0:01:28.65,Default,,0000,0000,0000,,you just get rid of the precent sign \Nand put it over 100.\N
Dialogue: 0,0:01:28.66,0:01:37.56,Default,,0000,0000,0000,,So 35.7% is the same thing as 35.7/100.
Dialogue: 0,0:01:37.59,0:01:41.47,Default,,0000,0000,0000,,Like 5%, that's the same thing as 5/100 \N
Dialogue: 0,0:01:41.50,0:01:44.68,Default,,0000,0000,0000,,or 50% is just the same thing as 50/100.
Dialogue: 0,0:01:44.73,0:01:53.51,Default,,0000,0000,0000,,So 35.7/100, well, that just equals 0.357.
Dialogue: 0,0:01:53.57,0:01:54.89,Default,,0000,0000,0000,,If this got you a little confused
Dialogue: 0,0:01:54.97,0:01:59.16,Default,,0000,0000,0000,,another way to think about percentage points is \Nif I write 35.7%,
Dialogue: 0,0:01:59.19,0:02:03.02,Default,,0000,0000,0000,,all you have to do is get rid of the percent sign
Dialogue: 0,0:02:03.08,0:02:07.27,Default,,0000,0000,0000,,and move the decimal to the left two spaces \N
Dialogue: 0,0:02:07.32,0:02:09.62,Default,,0000,0000,0000,,and it becomes 0.357
Dialogue: 0,0:02:09.71,0:02:11.84,Default,,0000,0000,0000,,Let me give you a couple of \Nmore examples down here.
Dialogue: 0,0:02:11.88,0:02:14.34,Default,,0000,0000,0000,,Let's say I had 5%.
Dialogue: 0,0:02:14.40,0:02:19.62,Default,,0000,0000,0000,,That is the same thing as 5/100.
Dialogue: 0,0:02:19.66,0:02:22.41,Default,,0000,0000,0000,,Or if you do the decimal technique, 5%,
Dialogue: 0,0:02:22.43,0:02:24.51,Default,,0000,0000,0000,,you could just move the decimal \Nand you get rid of the percent.
Dialogue: 0,0:02:24.63,0:02:28.60,Default,,0000,0000,0000,,And you move the decimal over 1 and 2, \Nand you put a 0 here.\N
Dialogue: 0,0:02:28.65,0:02:29.92,Default,,0000,0000,0000,,It's 0.05.
Dialogue: 0,0:02:29.97,0:02:32.37,Default,,0000,0000,0000,,And that's the same thing as 0.05.\N
Dialogue: 0,0:02:32.42,0:02:36.15,Default,,0000,0000,0000,,You also know that 0.05 and\N5/100 are the same thing.
Dialogue: 0,0:02:36.17,0:02:37.72,Default,,0000,0000,0000,,So let's get back to the problem.
Dialogue: 0,0:02:37.76,0:02:40.59,Default,,0000,0000,0000,,I hope that distraction didn't distract you too much.
Dialogue: 0,0:02:40.61,0:02:42.51,Default,,0000,0000,0000,,Scratch out all this.\N
Dialogue: 0,0:02:42.54,0:02:47.67,Default,,0000,0000,0000,,So 35.7% is equal to 0.357.\N
Dialogue: 0,0:02:47.69,0:02:51.77,Default,,0000,0000,0000,,Similarly, 108.1%.\N
Dialogue: 0,0:02:51.79,0:02:53.74,Default,,0000,0000,0000,,Let's to the technique where \Nwe just get rid of the percent
Dialogue: 0,0:02:53.77,0:02:59.14,Default,,0000,0000,0000,,and move the decimal space over \N1,2 spaces to the left.
Dialogue: 0,0:02:59.14,0:03:05.98,Default,,0000,0000,0000,,So then that equals 1.081.
Dialogue: 0,0:03:05.98,0:03:10.100,Default,,0000,0000,0000,,See we already know that this is samller than this.
Dialogue: 0,0:03:11.03,0:03:13.96,Default,,0000,0000,0000,,Well the next one is easy,\Nit's already in decimal form.
Dialogue: 0,0:03:14.02,0:03:16.37,Default,,0000,0000,0000,,0.5 is just going to be equal to 0.5.
Dialogue: 0,0:03:16.40,0:03:20.94,Default,,0000,0000,0000,,Now 13/93.
Dialogue: 0,0:03:20.100,0:03:23.71,Default,,0000,0000,0000,,To convert a fraction into a decimal
Dialogue: 0,0:03:23.74,0:03:27.16,Default,,0000,0000,0000,,we just take the denominator \Nand divide it into the numerator.
Dialogue: 0,0:03:27.17,0:03:28.34,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:03:28.35,0:03:33.52,Default,,0000,0000,0000,,93 goes into 13?\N
Dialogue: 0,0:03:33.53,0:03:39.39,Default,,0000,0000,0000,,Well, we know it goes into 13 zero times. Right?
Dialogue: 0,0:03:39.42,0:03:42.08,Default,,0000,0000,0000,,So let's add a decimal point here.
Dialogue: 0,0:03:42.10,0:03:47.18,Default,,0000,0000,0000,,So how many times does 93 go into 130?
Dialogue: 0,0:03:47.23,0:03:48.84,Default,,0000,0000,0000,,Well, it goes into it one time.
Dialogue: 0,0:03:48.85,0:03:52.07,Default,,0000,0000,0000,,1 times 93 is 93.
Dialogue: 0,0:03:52.11,0:03:56.04,Default,,0000,0000,0000,,Becomes a 10.
Dialogue: 0,0:03:56.10,0:03:58.45,Default,,0000,0000,0000,,That becomes a 2.
Dialogue: 0,0:03:58.48,0:04:02.06,Default,,0000,0000,0000,,Then we're going to borrow, we get 37.
Dialogue: 0,0:04:02.09,0:04:05.07,Default,,0000,0000,0000,,Bring down a 0.
Dialogue: 0,0:04:05.09,0:04:09.51,Default,,0000,0000,0000,,So 93 goes into 370?
Dialogue: 0,0:04:09.52,0:04:10.65,Default,,0000,0000,0000,,Let's see
Dialogue: 0,0:04:10.66,0:04:14.72,Default,,0000,0000,0000,,4 times 93 would be 372, so it actually goes into
Dialogue: 0,0:04:14.74,0:04:15.88,Default,,0000,0000,0000,,it only three times.
Dialogue: 0,0:04:15.88,0:04:21.78,Default,,0000,0000,0000,,3 times 3 is 9.
Dialogue: 0,0:04:21.81,0:04:25.68,Default,,0000,0000,0000,,3 times 9 is 27.
Dialogue: 0,0:04:25.70,0:04:30.82,Default,,0000,0000,0000,,So this equals?
Dialogue: 0,0:04:30.87,0:04:37.43,Default,,0000,0000,0000,,Let's see, this equals--if we say\Nthat this 0 becomes a 10.
Dialogue: 0,0:04:37.45,0:04:39.44,Default,,0000,0000,0000,,This become a 16.
Dialogue: 0,0:04:39.47,0:04:41.25,Default,,0000,0000,0000,,This becomes a 2.
Dialogue: 0,0:04:41.29,0:04:44.09,Default,,0000,0000,0000,,81.
Dialogue: 0,0:04:44.10,0:04:47.80,Default,,0000,0000,0000,,And then we say, how many times\Ndoes 93 go into 810?
Dialogue: 0,0:04:47.80,0:04:49.75,Default,,0000,0000,0000,,It goes roughly 8 times.
Dialogue: 0,0:04:49.75,0:04:51.90,Default,,0000,0000,0000,,And we could actually keep going, \N
Dialogue: 0,0:04:51.94,0:04:53.97,Default,,0000,0000,0000,,but for the sake of comparing these numbers,
Dialogue: 0,0:04:53.97,0:04:57.51,Default,,0000,0000,0000,,we've already gotten to a \Npretty good level of accuracy.\N
Dialogue: 0,0:04:57.56,0:04:59.100,Default,,0000,0000,0000,,So let's just stop this problem here \N
Dialogue: 0,0:04:59.100,0:05:01.49,Default,,0000,0000,0000,,because the decimal numbers could keep going on,
Dialogue: 0,0:05:01.54,0:05:02.79,Default,,0000,0000,0000,,but for the sake of comparison\N
Dialogue: 0,0:05:02.82,0:05:04.100,Default,,0000,0000,0000,,I think we've already got a good \Nsense of what this decimal looks like.
Dialogue: 0,0:05:04.100,0:05:09.60,Default,,0000,0000,0000,,It's 0.138 and then it'll just keep going.
Dialogue: 0,0:05:09.60,0:05:11.59,Default,,0000,0000,0000,,So let's write that down.
Dialogue: 0,0:05:11.59,0:05:15.35,Default,,0000,0000,0000,,And then finally, we have this mixed number here.
Dialogue: 0,0:05:15.39,0:05:16.55,Default,,0000,0000,0000,,And let me erase some of my work
Dialogue: 0,0:05:16.57,0:05:18.65,Default,,0000,0000,0000,,because I don't want to confuse you.
Dialogue: 0,0:05:18.67,0:05:21.03,Default,,0000,0000,0000,,Actually, let me keep it the way it is right now.
Dialogue: 0,0:05:21.09,0:05:21.74,Default,,0000,0000,0000,,So these two ways\N
Dialogue: 0,0:05:21.77,0:05:25.44,Default,,0000,0000,0000,,the easiest way to convert a \Nmixed number into a decimal is
Dialogue: 0,0:05:25.44,0:05:29.53,Default,,0000,0000,0000,,to just say, OK, this is 1 and then some fraction
Dialogue: 0,0:05:29.58,0:05:32.60,Default,,0000,0000,0000,,that's less than 1.
Dialogue: 0,0:05:32.62,0:05:36.41,Default,,0000,0000,0000,,Or we could convert it to a fraction, \Nan improper fraction\N
Dialogue: 0,0:05:36.43,0:05:38.79,Default,,0000,0000,0000,,like--oh, actually there are \Nno improper fractions here.\N
Dialogue: 0,0:05:38.87,0:05:39.63,Default,,0000,0000,0000,,Actually, let's do it that way.
Dialogue: 0,0:05:39.66,0:05:41.04,Default,,0000,0000,0000,,Let's convert to an improper fraction
Dialogue: 0,0:05:41.04,0:05:42.41,Default,,0000,0000,0000,,and then convert that into a decimal.
Dialogue: 0,0:05:42.49,0:05:45.79,Default,,0000,0000,0000,,Actually, I think I'm going to need more space,
Dialogue: 0,0:05:45.81,0:05:48.90,Default,,0000,0000,0000,,so let me clean up this a little bit.
Dialogue: 0,0:05:48.96,0:06:00.53,Default,,0000,0000,0000,,There we have a little more space to work with now.
Dialogue: 0,0:06:00.55,0:06:08.29,Default,,0000,0000,0000,,So 1 and 7/68.
Dialogue: 0,0:06:08.37,0:06:12.46,Default,,0000,0000,0000,,So to go from a mixed number to\Nan improper fraction,
Dialogue: 0,0:06:12.48,0:06:16.84,Default,,0000,0000,0000,,what you do is you take the 68 times 1
Dialogue: 0,0:06:16.86,0:06:19.63,Default,,0000,0000,0000,,and add it to the numerator here.\N
Dialogue: 0,0:06:19.68,0:06:20.81,Default,,0000,0000,0000,,And why does this make sense?
Dialogue: 0,0:06:20.87,0:06:26.24,Default,,0000,0000,0000,,Because this is the same thing as 1 plus 7/68. Right?
Dialogue: 0,0:06:26.28,0:06:28.98,Default,,0000,0000,0000,,1 and 7/68 is the same thing as 1 plus 7/68.\N
Dialogue: 0,0:06:29.01,0:06:31.54,Default,,0000,0000,0000,,And that's the same thing as you know
Dialogue: 0,0:06:31.54,0:06:39.27,Default,,0000,0000,0000,,from the fractions module, as 68/68 plus 7/68.
Dialogue: 0,0:06:39.32,0:06:47.26,Default,,0000,0000,0000,,And that's the same thing as 68 plus 7--75/68.\N
Dialogue: 0,0:06:47.29,0:06:51.64,Default,,0000,0000,0000,,So 1 and 7/68 is equal to 75/68.\N
Dialogue: 0,0:06:51.67,0:06:54.10,Default,,0000,0000,0000,,And now we convert this to a decimal \N
Dialogue: 0,0:06:54.10,0:06:56.29,Default,,0000,0000,0000,,using the technique we did for 13/93.\N
Dialogue: 0,0:06:56.37,0:06:58.60,Default,,0000,0000,0000,,So we say--let me get some space.
Dialogue: 0,0:06:58.61,0:07:04.26,Default,,0000,0000,0000,,We say 68 goes into 75
Dialogue: 0,0:07:04.31,0:07:06.10,Default,,0000,0000,0000,,suspicion I'm going to run out of space.\N
Dialogue: 0,0:07:06.12,0:07:09.22,Default,,0000,0000,0000,,68 goes into 75 one time.\N
Dialogue: 0,0:07:09.22,0:07:13.08,Default,,0000,0000,0000,,1 times 68 is 68.
Dialogue: 0,0:07:13.11,0:07:15.68,Default,,0000,0000,0000,,75 minus 68 is 7.
Dialogue: 0,0:07:15.71,0:07:17.27,Default,,0000,0000,0000,,Bring down the 0.
Dialogue: 0,0:07:17.30,0:07:19.54,Default,,0000,0000,0000,,Actually, you don't have to write the decimal there.
Dialogue: 0,0:07:19.58,0:07:20.92,Default,,0000,0000,0000,,Ignore that decimal.
Dialogue: 0,0:07:20.94,0:07:23.58,Default,,0000,0000,0000,,68 goes into 70 one time.
Dialogue: 0,0:07:23.60,0:07:26.11,Default,,0000,0000,0000,,1 times 68 is 68.
Dialogue: 0,0:07:26.13,0:07:30.42,Default,,0000,0000,0000,,70 minus 68 is 2, bring down another 0. \N
Dialogue: 0,0:07:30.45,0:07:32.94,Default,,0000,0000,0000,,68 goes into 20 zero times.\N
Dialogue: 0,0:07:32.97,0:07:35.05,Default,,0000,0000,0000,,And the problem's going to keep going on,
Dialogue: 0,0:07:35.05,0:07:37.35,Default,,0000,0000,0000,,but I think we've already once again,
Dialogue: 0,0:07:37.36,0:07:39.77,Default,,0000,0000,0000,,gotten to enough accuracy that we can compare.\N
Dialogue: 0,0:07:39.83,0:07:47.36,Default,,0000,0000,0000,,So 1 and 7/68 we've now figured out is equal to 1.10
Dialogue: 0,0:07:47.36,0:07:51.56,Default,,0000,0000,0000,,and if we kept dividing we'll keep \Ngetting more decimals of accuracy, \N
Dialogue: 0,0:07:51.60,0:07:53.12,Default,,0000,0000,0000,,but I think we're now ready to compare.\N
Dialogue: 0,0:07:53.18,0:07:56.12,Default,,0000,0000,0000,,So all of these numbers I just \Nrewrote them as decimals.
Dialogue: 0,0:07:56.15,0:08:00.07,Default,,0000,0000,0000,,So 35.7% is 0.357.
Dialogue: 0,0:08:00.08,0:08:04.37,Default,,0000,0000,0000,,108.1%--ignore this for now \N
Dialogue: 0,0:08:04.41,0:08:05.58,Default,,0000,0000,0000,,because we just used that to do the work.\N
Dialogue: 0,0:08:05.62,0:08:09.28,Default,,0000,0000,0000,,It's 108.1% is equal to 1.081.\N
Dialogue: 0,0:08:09.31,0:08:10.76,Default,,0000,0000,0000,,0.5 is 0.5.
Dialogue: 0,0:08:10.80,0:08:15.13,Default,,0000,0000,0000,,13/93 is 0.138.
Dialogue: 0,0:08:15.17,0:08:19.92,Default,,0000,0000,0000,,And 1 and 7/68 is 1.10 and it'll keep going on.\N
Dialogue: 0,0:08:19.94,0:08:22.56,Default,,0000,0000,0000,,So what's the samllest?
Dialogue: 0,0:08:22.61,0:08:25.29,Default,,0000,0000,0000,,So the samllest is 0.
Dialogue: 0,0:08:25.31,0:08:27.35,Default,,0000,0000,0000,,Actually, the smallest is right here.\N
Dialogue: 0,0:08:27.38,0:08:31.38,Default,,0000,0000,0000,,So I'm going to rank them from samllest to largest.
Dialogue: 0,0:08:31.41,0:08:35.54,Default,,0000,0000,0000,,So the samllest is 0.138.\N
Dialogue: 0,0:08:35.56,0:08:39.96,Default,,0000,0000,0000,,Then the next largest is going to be 0.357. Right?
Dialogue: 0,0:08:40.01,0:08:42.85,Default,,0000,0000,0000,,Then the next largest is going to be 0.5.\N
Dialogue: 0,0:08:42.86,0:08:46.22,Default,,0000,0000,0000,,Then you're going to have 1.08.\N
Dialogue: 0,0:08:46.27,0:08:51.35,Default,,0000,0000,0000,,And then you're going to have 1 and 7/68.
Dialogue: 0,0:08:51.36,0:08:56.50,Default,,0000,0000,0000,,So hopefully, actually, I'm going to \Ndo more examples of this,
Dialogue: 0,0:08:56.52,0:09:00.01,Default,,0000,0000,0000,,but for this video I think this\Nis the only one I have time for. \N
Dialogue: 0,0:09:00.02,0:09:01.83,Default,,0000,0000,0000,,But hopefully this gives you a \Nsense of doing these problems.
Dialogue: 0,0:09:01.86,0:09:05.11,Default,,0000,0000,0000,,I always find it easier to go into \Nthe decimal mode to compare.
Dialogue: 0,0:09:05.14,0:09:07.52,Default,,0000,0000,0000,,And actually, the hints on the module \Nwill be the same for you.
Dialogue: 0,0:09:07.55,0:09:10.79,Default,,0000,0000,0000,,But I think you're ready at least \Nnow to try the problems.
Dialogue: 0,0:09:10.83,0:09:12.41,Default,,0000,0000,0000,,If you're not, if you want to see other examples,
Dialogue: 0,0:09:12.44,0:09:15.03,Default,,0000,0000,0000,,you might just want to either re-watch this video
Dialogue: 0,0:09:15.05,0:09:19.85,Default,,0000,0000,0000,,and/or I might record some more videos \Nwith more examples right now.
Dialogue: 0,0:09:19.86,9:59:59.99,Default,,0000,0000,0000,,Anyway, have fun.