[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.91,0:00:04.36,Default,,0000,0000,0000,,Welcome to the presentation\Non ordering numbers.
Dialogue: 0,0:00:04.36,0:00:06.94,Default,,0000,0000,0000,,Let's get started with some\Nproblems that I think, as you
Dialogue: 0,0:00:06.94,0:00:09.27,Default,,0000,0000,0000,,go through the examples\Nhopefully, you'll understand
Dialogue: 0,0:00:09.27,0:00:10.91,Default,,0000,0000,0000,,how to do these problems.
Dialogue: 0,0:00:10.91,0:00:11.70,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:00:11.70,0:00:23.20,Default,,0000,0000,0000,,The first set of numbers that\Nwe have to order is 35.7%,
Dialogue: 0,0:00:23.20,0:00:44.59,Default,,0000,0000,0000,,108.1% 0.5, 13/93,\Nand 1 and 7/68.
Dialogue: 0,0:00:44.59,0:00:46.59,Default,,0000,0000,0000,,So let's do this problem.
Dialogue: 0,0:00:46.59,0:00:48.81,Default,,0000,0000,0000,,The important thing to remember\Nwhenever you're doing this type
Dialogue: 0,0:00:48.81,0:00:52.82,Default,,0000,0000,0000,,of ordering of numbers is to\Nrealize that these are all just
Dialogue: 0,0:00:52.82,0:00:56.94,Default,,0000,0000,0000,,different ways to represent--\Nthese are all a percent or a
Dialogue: 0,0:00:56.94,0:01:00.27,Default,,0000,0000,0000,,decimal or a fraction or a\Nmixed-- are all just different
Dialogue: 0,0:01:00.27,0:01:02.68,Default,,0000,0000,0000,,ways of representing numbers.
Dialogue: 0,0:01:02.68,0:01:05.11,Default,,0000,0000,0000,,It's very hard to compare when\Nyou just look at it like this,
Dialogue: 0,0:01:05.11,0:01:07.13,Default,,0000,0000,0000,,so what I like to do is I\Nlike to convert them
Dialogue: 0,0:01:07.13,0:01:08.19,Default,,0000,0000,0000,,all to decimals.
Dialogue: 0,0:01:08.19,0:01:11.10,Default,,0000,0000,0000,,But there could be someone who\Nlikes to convert them all to
Dialogue: 0,0:01:11.10,0:01:14.22,Default,,0000,0000,0000,,percentages or convert them all\Nto fractions and then compare.
Dialogue: 0,0:01:14.22,0:01:16.92,Default,,0000,0000,0000,,But I always find decimals to\Nbe the easiest way to compare.
Dialogue: 0,0:01:16.92,0:01:19.37,Default,,0000,0000,0000,,So let's start with this 35.7%.
Dialogue: 0,0:01:19.37,0:01:21.94,Default,,0000,0000,0000,,Let's turn this into a decimal.
Dialogue: 0,0:01:21.94,0:01:25.09,Default,,0000,0000,0000,,Well, the easiest thing to\Nremember is if you have a
Dialogue: 0,0:01:25.09,0:01:27.49,Default,,0000,0000,0000,,percent you just get rid of\Nthe percent sign and
Dialogue: 0,0:01:27.49,0:01:28.58,Default,,0000,0000,0000,,put it over 100.
Dialogue: 0,0:01:28.58,0:01:38.97,Default,,0000,0000,0000,,So 35.7% is the same\Nthing as 35.7/100.
Dialogue: 0,0:01:38.97,0:01:43.02,Default,,0000,0000,0000,,Like 5%, that's the same thing\Nas 5/100 or 50% is just
Dialogue: 0,0:01:43.02,0:01:45.05,Default,,0000,0000,0000,,the same thing as 50/100.
Dialogue: 0,0:01:45.05,0:01:53.99,Default,,0000,0000,0000,,So 35.7/100, well, that\Njust equals 0.357.
Dialogue: 0,0:01:53.99,0:01:55.73,Default,,0000,0000,0000,,If this got you a little\Nconfused another way to think
Dialogue: 0,0:01:55.73,0:02:01.97,Default,,0000,0000,0000,,about percentage points is if I\Nwrite 35.7%, all you have to do
Dialogue: 0,0:02:01.97,0:02:05.54,Default,,0000,0000,0000,,is get rid of the percent sign\Nand move the decimal to the
Dialogue: 0,0:02:05.54,0:02:10.14,Default,,0000,0000,0000,,left two spaces and\Nit becomes 0.357.
Dialogue: 0,0:02:10.14,0:02:11.87,Default,,0000,0000,0000,,Let me give you a couple of\Nmore examples down here.
Dialogue: 0,0:02:11.87,0:02:16.05,Default,,0000,0000,0000,,Let's say I had 5%.
Dialogue: 0,0:02:16.05,0:02:20.02,Default,,0000,0000,0000,,That is the same\Nthing as 5/100.
Dialogue: 0,0:02:20.02,0:02:22.67,Default,,0000,0000,0000,,Or if you do the decimal\Ntechnique, 5%, you could just
Dialogue: 0,0:02:22.67,0:02:24.73,Default,,0000,0000,0000,,move the decimal and you\Nget rid of the percent.
Dialogue: 0,0:02:24.73,0:02:28.63,Default,,0000,0000,0000,,And you move the decimal over 1\Nand 2, and you put a 0 here.
Dialogue: 0,0:02:28.63,0:02:30.37,Default,,0000,0000,0000,,It's 0.05.
Dialogue: 0,0:02:30.37,0:02:33.28,Default,,0000,0000,0000,,And that's the same\Nthing as 0.05.
Dialogue: 0,0:02:33.28,0:02:36.38,Default,,0000,0000,0000,,You also know that 0.05 and\N5/100 are the same thing.
Dialogue: 0,0:02:36.38,0:02:37.62,Default,,0000,0000,0000,,So let's get back\Nto the problem.
Dialogue: 0,0:02:37.62,0:02:40.77,Default,,0000,0000,0000,,I hope that distraction didn't\Ndistract you too much.
Dialogue: 0,0:02:40.77,0:02:43.19,Default,,0000,0000,0000,,Let me scratch out all this.
Dialogue: 0,0:02:43.19,0:02:49.05,Default,,0000,0000,0000,,So 35.7% is equal to 0.357.
Dialogue: 0,0:02:49.05,0:02:51.87,Default,,0000,0000,0000,,Similarly, 108.1%.
Dialogue: 0,0:02:51.87,0:02:54.08,Default,,0000,0000,0000,,Let's to the technique where we\Njust get rid of the percent and
Dialogue: 0,0:02:54.08,0:02:59.35,Default,,0000,0000,0000,,move the decimal space over\N1, 2 spaces to the left.
Dialogue: 0,0:02:59.35,0:03:08.60,Default,,0000,0000,0000,,So then that equals 1.081.
Dialogue: 0,0:03:08.60,0:03:11.57,Default,,0000,0000,0000,,See we already know that\Nthis is smaller than this.
Dialogue: 0,0:03:11.57,0:03:14.14,Default,,0000,0000,0000,,Well the next one is easy,\Nit's already in decimal form.
Dialogue: 0,0:03:14.14,0:03:16.04,Default,,0000,0000,0000,,0.5 is just going to\Nbe equal to 0.5.
Dialogue: 0,0:03:18.82,0:03:21.05,Default,,0000,0000,0000,,Now 13/93.
Dialogue: 0,0:03:21.05,0:03:24.34,Default,,0000,0000,0000,,To convert a fraction into\Na decimal we just take the
Dialogue: 0,0:03:24.34,0:03:27.32,Default,,0000,0000,0000,,denominator and divide\Nit into the numerator.
Dialogue: 0,0:03:27.32,0:03:29.35,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:03:29.35,0:03:33.02,Default,,0000,0000,0000,,93 goes into 13?
Dialogue: 0,0:03:36.53,0:03:39.76,Default,,0000,0000,0000,,Well, we know it goes\Ninto 13 zero times.
Dialogue: 0,0:03:39.76,0:03:43.99,Default,,0000,0000,0000,,So let's add a\Ndecimal point here.
Dialogue: 0,0:03:43.99,0:03:47.55,Default,,0000,0000,0000,,So how many times\Ndoes 93 go into 130?
Dialogue: 0,0:03:47.55,0:03:49.53,Default,,0000,0000,0000,,Well, it goes into it one time.
Dialogue: 0,0:03:49.53,0:03:51.41,Default,,0000,0000,0000,,1 times 93 is 93.
Dialogue: 0,0:03:55.06,0:03:56.55,Default,,0000,0000,0000,,Becomes a 10.
Dialogue: 0,0:03:56.55,0:03:58.96,Default,,0000,0000,0000,,That becomes a 2.
Dialogue: 0,0:03:58.96,0:04:03.70,Default,,0000,0000,0000,,Then we're going to\Nborrow, so get 37.
Dialogue: 0,0:04:03.70,0:04:06.59,Default,,0000,0000,0000,,Bring down a 0.
Dialogue: 0,0:04:06.59,0:04:10.01,Default,,0000,0000,0000,,So 93 goes into 370?
Dialogue: 0,0:04:10.01,0:04:10.47,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:04:10.47,0:04:14.79,Default,,0000,0000,0000,,4 times 93 would be 372,\Nso it actually goes into
Dialogue: 0,0:04:14.79,0:04:15.70,Default,,0000,0000,0000,,it only three times.
Dialogue: 0,0:04:19.39,0:04:22.88,Default,,0000,0000,0000,,3 times 3 is 9.
Dialogue: 0,0:04:22.88,0:04:25.27,Default,,0000,0000,0000,,3 times 9 is 27.
Dialogue: 0,0:04:30.11,0:04:31.60,Default,,0000,0000,0000,,So this equals?
Dialogue: 0,0:04:31.60,0:04:38.05,Default,,0000,0000,0000,,Let's see, this equals-- if we\Nsay that this 0 becomes a 10.
Dialogue: 0,0:04:38.05,0:04:39.62,Default,,0000,0000,0000,,This become a 16.
Dialogue: 0,0:04:39.62,0:04:42.44,Default,,0000,0000,0000,,This becomes a 2.
Dialogue: 0,0:04:42.44,0:04:45.21,Default,,0000,0000,0000,,81.
Dialogue: 0,0:04:45.21,0:04:48.12,Default,,0000,0000,0000,,And then we say, how many\Ntimes does 93 go into 810?
Dialogue: 0,0:04:48.12,0:04:50.86,Default,,0000,0000,0000,,It goes roughly 8 times.
Dialogue: 0,0:04:50.86,0:04:52.86,Default,,0000,0000,0000,,And we could actually keep\Ngoing, but for the sake of
Dialogue: 0,0:04:52.86,0:04:55.64,Default,,0000,0000,0000,,comparing these numbers, we've\Nalready gotten to a pretty
Dialogue: 0,0:04:55.64,0:04:57.58,Default,,0000,0000,0000,,good level of accuracy.
Dialogue: 0,0:04:57.58,0:05:00.74,Default,,0000,0000,0000,,So let's just stop this problem\Nhere because the decimal
Dialogue: 0,0:05:00.74,0:05:02.72,Default,,0000,0000,0000,,numbers could keep going on,\Nbut for the sake of comparison
Dialogue: 0,0:05:02.72,0:05:04.41,Default,,0000,0000,0000,,I think we've already got a\Ngood sense of what this
Dialogue: 0,0:05:04.41,0:05:05.36,Default,,0000,0000,0000,,decimal looks like.
Dialogue: 0,0:05:05.36,0:05:10.33,Default,,0000,0000,0000,,It's 0.138 and then\Nit'll just keep going.
Dialogue: 0,0:05:10.33,0:05:13.01,Default,,0000,0000,0000,,So let's write that down.
Dialogue: 0,0:05:13.01,0:05:15.34,Default,,0000,0000,0000,,And then finally, we have\Nthis mixed number here.
Dialogue: 0,0:05:15.34,0:05:18.07,Default,,0000,0000,0000,,And let me erase some of\Nmy work because I don't
Dialogue: 0,0:05:18.07,0:05:18.84,Default,,0000,0000,0000,,want to confuse you.
Dialogue: 0,0:05:18.84,0:05:22.70,Default,,0000,0000,0000,,Actually, let me keep it\Nthe way it is right now.
Dialogue: 0,0:05:22.70,0:05:26.12,Default,,0000,0000,0000,,The easiest way to convert a\Nmixed number into a decimal is
Dialogue: 0,0:05:26.12,0:05:29.63,Default,,0000,0000,0000,,to just say, OK, this is 1\Nand then some fraction
Dialogue: 0,0:05:29.63,0:05:32.92,Default,,0000,0000,0000,,that's less than 1.
Dialogue: 0,0:05:32.92,0:05:36.42,Default,,0000,0000,0000,,Or we could convert it to a\Nfraction, an improper fraction
Dialogue: 0,0:05:36.42,0:05:38.79,Default,,0000,0000,0000,,like-- oh, actually there are\Nno improper fractions here.
Dialogue: 0,0:05:38.79,0:05:39.64,Default,,0000,0000,0000,,Actually, let's do it that way.
Dialogue: 0,0:05:39.64,0:05:41.63,Default,,0000,0000,0000,,Let's convert to an improper\Nfraction and then convert
Dialogue: 0,0:05:41.63,0:05:44.11,Default,,0000,0000,0000,,that into a decimal.
Dialogue: 0,0:05:44.11,0:05:46.06,Default,,0000,0000,0000,,Actually, I think I'm going to\Nneed more space, so let me
Dialogue: 0,0:05:46.06,0:05:48.74,Default,,0000,0000,0000,,clean up this a little bit.
Dialogue: 0,0:05:58.24,0:05:58.60,Default,,0000,0000,0000,,There.
Dialogue: 0,0:05:58.60,0:06:01.04,Default,,0000,0000,0000,,We have a little more\Nspace to work with now.
Dialogue: 0,0:06:04.26,0:06:08.57,Default,,0000,0000,0000,,So 1 and 7/68.
Dialogue: 0,0:06:08.57,0:06:13.70,Default,,0000,0000,0000,,So to go from a mixed number to\Nan improper fraction, what you
Dialogue: 0,0:06:13.70,0:06:18.76,Default,,0000,0000,0000,,do is you take the 68 times 1\Nand add it to the
Dialogue: 0,0:06:18.76,0:06:19.72,Default,,0000,0000,0000,,numerator here.
Dialogue: 0,0:06:19.72,0:06:21.00,Default,,0000,0000,0000,,And why does this make sense?
Dialogue: 0,0:06:21.00,0:06:26.12,Default,,0000,0000,0000,,Because this is the same\Nthing as 1 plus 7/68.
Dialogue: 0,0:06:26.12,0:06:29.68,Default,,0000,0000,0000,,1 and 7/68 is the same\Nthing as 1 plus 7/68.
Dialogue: 0,0:06:29.68,0:06:32.80,Default,,0000,0000,0000,,And that's the same thing as\Nyou know from the fractions
Dialogue: 0,0:06:32.80,0:06:40.33,Default,,0000,0000,0000,,module, as 68/68 plus 7/68.
Dialogue: 0,0:06:40.33,0:06:47.65,Default,,0000,0000,0000,,And that's the same thing\Nas 68 plus 7-- 75/68.
Dialogue: 0,0:06:47.65,0:06:51.79,Default,,0000,0000,0000,,So 1 and 7/68 is\Nequal to 75/68.
Dialogue: 0,0:06:51.79,0:06:54.87,Default,,0000,0000,0000,,And now we convert this to a\Ndecimal using the technique
Dialogue: 0,0:06:54.87,0:06:56.35,Default,,0000,0000,0000,,we did for 13/93.
Dialogue: 0,0:06:56.35,0:06:58.57,Default,,0000,0000,0000,,So we say-- let me\Nget some space.
Dialogue: 0,0:06:58.57,0:07:05.00,Default,,0000,0000,0000,,We say 68 goes into 75--\Nsuspicion I'm going
Dialogue: 0,0:07:05.00,0:07:07.36,Default,,0000,0000,0000,,to run out of space.
Dialogue: 0,0:07:07.36,0:07:09.16,Default,,0000,0000,0000,,68 goes into 75 one time.
Dialogue: 0,0:07:09.16,0:07:13.29,Default,,0000,0000,0000,,1 times 68 is 68.
Dialogue: 0,0:07:13.29,0:07:16.46,Default,,0000,0000,0000,,75 minus 68 is 7.
Dialogue: 0,0:07:16.46,0:07:17.35,Default,,0000,0000,0000,,Bring down the 0.
Dialogue: 0,0:07:17.35,0:07:20.49,Default,,0000,0000,0000,,Actually, you don't have to\Nwrite the decimal there.
Dialogue: 0,0:07:20.49,0:07:21.10,Default,,0000,0000,0000,,Ignore that decimal.
Dialogue: 0,0:07:21.10,0:07:24.40,Default,,0000,0000,0000,,68 goes into 70 one time.
Dialogue: 0,0:07:24.40,0:07:28.15,Default,,0000,0000,0000,,1 times 68 is 68.
Dialogue: 0,0:07:28.15,0:07:30.99,Default,,0000,0000,0000,,70 minus 68 is 2,\Nbring down another 0.
Dialogue: 0,0:07:30.99,0:07:33.24,Default,,0000,0000,0000,,68 goes into 20 zero times.
Dialogue: 0,0:07:33.24,0:07:36.55,Default,,0000,0000,0000,,And the problem's going to keep\Ngoing on, but I think we've
Dialogue: 0,0:07:36.55,0:07:38.99,Default,,0000,0000,0000,,already once again, gotten to\Nenough accuracy that
Dialogue: 0,0:07:38.99,0:07:40.04,Default,,0000,0000,0000,,we can compare.
Dialogue: 0,0:07:40.04,0:07:48.32,Default,,0000,0000,0000,,So 1 and 7/68 we've now figured\Nout is equal to 1.10-- and if
Dialogue: 0,0:07:48.32,0:07:51.00,Default,,0000,0000,0000,,we kept dividing we'll keep\Ngetting more decimals of
Dialogue: 0,0:07:51.00,0:07:53.51,Default,,0000,0000,0000,,accuracy, but I think we're\Nnow ready to compare.
Dialogue: 0,0:07:53.51,0:07:56.55,Default,,0000,0000,0000,,So all of these numbers I just\Nrewrote them as decimals.
Dialogue: 0,0:07:56.55,0:08:00.55,Default,,0000,0000,0000,,So 35.7% is 0.357.
Dialogue: 0,0:08:00.55,0:08:05.00,Default,,0000,0000,0000,,108.1%-- ignore this for\Nnow because we just used
Dialogue: 0,0:08:05.00,0:08:05.72,Default,,0000,0000,0000,,that to do the work.
Dialogue: 0,0:08:05.72,0:08:09.66,Default,,0000,0000,0000,,It's 108.1% is equal to 1.081.
Dialogue: 0,0:08:09.66,0:08:11.26,Default,,0000,0000,0000,,0.5 is 0.5.
Dialogue: 0,0:08:11.26,0:08:15.77,Default,,0000,0000,0000,,13/93 is 0.138.
Dialogue: 0,0:08:15.77,0:08:20.85,Default,,0000,0000,0000,,And 1 and 7/68 is 1.10\Nand it'll keep going on.
Dialogue: 0,0:08:20.85,0:08:23.01,Default,,0000,0000,0000,,So what's the smallest?
Dialogue: 0,0:08:23.01,0:08:26.32,Default,,0000,0000,0000,,So the smallest is\N0.-- actually, no.
Dialogue: 0,0:08:26.32,0:08:28.30,Default,,0000,0000,0000,,The smallest is right here.
Dialogue: 0,0:08:28.30,0:08:31.45,Default,,0000,0000,0000,,So I'm going to rank them\Nfrom smallest to largest.
Dialogue: 0,0:08:31.45,0:08:36.25,Default,,0000,0000,0000,,So the smallest is 0.138.
Dialogue: 0,0:08:36.25,0:08:40.64,Default,,0000,0000,0000,,Then the next largest\Nis going to be 0.357.
Dialogue: 0,0:08:40.64,0:08:44.47,Default,,0000,0000,0000,,Then the next largest\Nis going to be 0.5.
Dialogue: 0,0:08:44.47,0:08:47.46,Default,,0000,0000,0000,,Then you're going to have 1.08.
Dialogue: 0,0:08:47.46,0:08:54.62,Default,,0000,0000,0000,,And then you're going\Nto have 1 and 7/68.
Dialogue: 0,0:08:54.62,0:08:56.84,Default,,0000,0000,0000,,Well, actually, I'm going to do\Nmore examples of this, but for
Dialogue: 0,0:08:56.84,0:08:59.89,Default,,0000,0000,0000,,this video I think this is the\Nonly one I have time for.
Dialogue: 0,0:08:59.89,0:09:01.91,Default,,0000,0000,0000,,But hopefully this gives you a\Nsense of doing these problems.
Dialogue: 0,0:09:01.91,0:09:04.37,Default,,0000,0000,0000,,I always find it easier\Nto go into the decimal
Dialogue: 0,0:09:04.37,0:09:05.28,Default,,0000,0000,0000,,mode to compare.
Dialogue: 0,0:09:05.28,0:09:06.68,Default,,0000,0000,0000,,And actually, the hints\Non the module will
Dialogue: 0,0:09:06.68,0:09:08.67,Default,,0000,0000,0000,,be the same for you.
Dialogue: 0,0:09:08.67,0:09:11.04,Default,,0000,0000,0000,,But I think you're ready at\Nleast now to try the problems.
Dialogue: 0,0:09:11.04,0:09:13.17,Default,,0000,0000,0000,,If you're not, if you want to\Nsee other examples, you might
Dialogue: 0,0:09:13.17,0:09:16.83,Default,,0000,0000,0000,,just want to either re-watch\Nthis video and/or I might
Dialogue: 0,0:09:16.83,0:09:20.53,Default,,0000,0000,0000,,record some more videos with\Nmore examples right now.
Dialogue: 0,0:09:20.53,0:09:22.56,Default,,0000,0000,0000,,Anyway, have fun.