[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.88,0:00:03.31,Default,,0000,0000,0000,,Welcome to the\Npresentation on units.
Dialogue: 0,0:00:03.31,0:00:05.39,Default,,0000,0000,0000,,Let's get started.
Dialogue: 0,0:00:05.39,0:00:12.77,Default,,0000,0000,0000,,So if I were to ask you, or if\NI were to say, I have traveled
Dialogue: 0,0:00:12.77,0:00:20.91,Default,,0000,0000,0000,,0.05 kilometers-- some\Npeople say KIL-ometers
Dialogue: 0,0:00:20.91,0:00:22.02,Default,,0000,0000,0000,,or kil-O-meters.
Dialogue: 0,0:00:22.02,0:00:23.44,Default,,0000,0000,0000,,
Dialogue: 0,0:00:23.44,0:00:24.85,Default,,0000,0000,0000,,If I have traveled 0.05\Nkilometers, how many
Dialogue: 0,0:00:28.25,0:00:30.86,Default,,0000,0000,0000,,centimeters have I traveled?
Dialogue: 0,0:00:30.86,0:00:32.59,Default,,0000,0000,0000,,That's question\Nmark centimeters.
Dialogue: 0,0:00:32.59,0:00:35.88,Default,,0000,0000,0000,,So before we break into the\Nmath, it's important to just
Dialogue: 0,0:00:38.39,0:00:41.73,Default,,0000,0000,0000,,know what these prefixes\Ncenti and kilo mean.
Dialogue: 0,0:00:41.73,0:00:44.65,Default,,0000,0000,0000,,And it's good to memorize this,\Nor when you're first starting
Dialogue: 0,0:00:44.65,0:00:46.13,Default,,0000,0000,0000,,to do these problems, you can\Njust write them down on a piece
Dialogue: 0,0:00:46.13,0:00:48.08,Default,,0000,0000,0000,,of paper, just so you\Nhave a reference.
Dialogue: 0,0:00:48.08,0:01:06.46,Default,,0000,0000,0000,,So kilo means 1,000, hecto\Nmeans 100, deca means 10.
Dialogue: 0,0:01:06.46,0:01:09.84,Default,,0000,0000,0000,,You might recognize that\Nfrom decade, 10 years.
Dialogue: 0,0:01:09.84,0:01:13.98,Default,,0000,0000,0000,,And then, of course, you\Nhave no prefix, means 1.
Dialogue: 0,0:01:13.98,0:01:15.58,Default,,0000,0000,0000,,No prefix.
Dialogue: 0,0:01:15.58,0:01:18.71,Default,,0000,0000,0000,,No prefix equals 1.
Dialogue: 0,0:01:18.71,0:01:28.10,Default,,0000,0000,0000,,deci is equal to 0.1 or 1/10.
Dialogue: 0,0:01:28.10,0:01:32.51,Default,,0000,0000,0000,,centi-- I keep changing\Nbetween cases.
Dialogue: 0,0:01:32.51,0:01:38.59,Default,,0000,0000,0000,,centi is equal to\N0.01, or 1/100.
Dialogue: 0,0:01:38.59,0:01:45.11,Default,,0000,0000,0000,,And then milli is equal\Nto 0.001, and that's the
Dialogue: 0,0:01:45.11,0:01:48.71,Default,,0000,0000,0000,,same thing as 1/1,000.
Dialogue: 0,0:01:48.71,0:01:52.81,Default,,0000,0000,0000,,And the way I remember, I mean,\Ncenti, if you think of a
Dialogue: 0,0:01:52.81,0:01:54.74,Default,,0000,0000,0000,,centipede, it has a 100 feet.
Dialogue: 0,0:01:54.74,0:01:58.36,Default,,0000,0000,0000,,A millipede, I'm not sure if a\Nmillipede has 1,000 feet, but
Dialogue: 0,0:01:58.36,0:02:00.85,Default,,0000,0000,0000,,that's the implication when\Nsomeone says a millipede
Dialogue: 0,0:02:00.85,0:02:02.55,Default,,0000,0000,0000,,because pede means feet.
Dialogue: 0,0:02:02.55,0:02:03.81,Default,,0000,0000,0000,,So let's go back\Nto the problem.
Dialogue: 0,0:02:03.81,0:02:08.49,Default,,0000,0000,0000,,If I have 0.05 kilometers, how\Nmany centimeters do I have?
Dialogue: 0,0:02:08.49,0:02:10.35,Default,,0000,0000,0000,,Whenever I do a problem like\Nthis, I like to actually
Dialogue: 0,0:02:10.35,0:02:12.93,Default,,0000,0000,0000,,convert my number to\Nmeters because that's
Dialogue: 0,0:02:12.93,0:02:14.29,Default,,0000,0000,0000,,very easy for me.
Dialogue: 0,0:02:14.29,0:02:18.15,Default,,0000,0000,0000,,And actually, I'm going to\Nabbreviate this is km, and
Dialogue: 0,0:02:18.15,0:02:21.53,Default,,0000,0000,0000,,we can abbreviate this\Nas cm for centimeters.
Dialogue: 0,0:02:21.53,0:02:28.48,Default,,0000,0000,0000,,So let's say 0.05 km.
Dialogue: 0,0:02:28.48,0:02:32.50,Default,,0000,0000,0000,,Well, if I want to convert this\Ninto meters, is it going to be
Dialogue: 0,0:02:32.50,0:02:37.15,Default,,0000,0000,0000,,more than 0.05 meters\Nor less than 0.05?
Dialogue: 0,0:02:37.15,0:02:40.82,Default,,0000,0000,0000,,Well, a kilometer is a very\Nlarge distance, so in terms
Dialogue: 0,0:02:40.82,0:02:43.43,Default,,0000,0000,0000,,of meters, it's going to\Nbe a much bigger number.
Dialogue: 0,0:02:43.43,0:02:52.60,Default,,0000,0000,0000,,So we can multiply this times\N1,000 meters, and I'll do
Dialogue: 0,0:02:52.60,0:02:53.88,Default,,0000,0000,0000,,it over 1, per kilometer.
Dialogue: 0,0:02:53.88,0:02:56.49,Default,,0000,0000,0000,,And what does that get?
Dialogue: 0,0:02:58.05,0:03:04.89,Default,,0000,0000,0000,,Well, 0.05 times 1,000\Nis equal to 50, right?
Dialogue: 0,0:03:04.89,0:03:07.67,Default,,0000,0000,0000,,I just multiplied\N0.05 times 1,000.
Dialogue: 0,0:03:07.67,0:03:12.61,Default,,0000,0000,0000,,And with the units, I now\Nhave kilometers times
Dialogue: 0,0:03:12.61,0:03:16.26,Default,,0000,0000,0000,,meters over kilometers.
Dialogue: 0,0:03:16.26,0:03:18.29,Default,,0000,0000,0000,,And the kilometers cancel out.
Dialogue: 0,0:03:18.29,0:03:22.26,Default,,0000,0000,0000,,And just so you're familiar\Nwith this, you can treat units
Dialogue: 0,0:03:22.26,0:03:24.64,Default,,0000,0000,0000,,exactly the same way that you\Nwould treat numbers
Dialogue: 0,0:03:24.64,0:03:25.67,Default,,0000,0000,0000,,or variables.
Dialogue: 0,0:03:25.67,0:03:28.99,Default,,0000,0000,0000,,As long as you have the same\Nunit in the numerator and the
Dialogue: 0,0:03:28.99,0:03:30.97,Default,,0000,0000,0000,,denominator, you can cancel\Nthem out, assuming that you're
Dialogue: 0,0:03:30.97,0:03:33.49,Default,,0000,0000,0000,,not adding units, you're\Nmultiplying units.
Dialogue: 0,0:03:33.49,0:03:36.54,Default,,0000,0000,0000,,So you have kilometers times\Nmeters divided by kilometers,
Dialogue: 0,0:03:36.54,0:03:40.03,Default,,0000,0000,0000,,and that equals 50 meters.
Dialogue: 0,0:03:40.03,0:03:43.89,Default,,0000,0000,0000,,And it's good to always do a\Nreality check after every step.
Dialogue: 0,0:03:43.89,0:03:45.70,Default,,0000,0000,0000,,Usually when you do these types\Nof problems, you know, OK, if I
Dialogue: 0,0:03:45.70,0:03:48.78,Default,,0000,0000,0000,,want to go from kilometers to\Nmeters, I'm going to use the
Dialogue: 0,0:03:48.78,0:03:51.01,Default,,0000,0000,0000,,number 1,000, because that's\Nthe relationship between
Dialogue: 0,0:03:51.01,0:03:52.17,Default,,0000,0000,0000,,a kilometer and a meter.
Dialogue: 0,0:03:52.17,0:03:54.83,Default,,0000,0000,0000,,And you're always confused,\Nwell, do I multiply by 1,000,
Dialogue: 0,0:03:54.83,0:03:56.25,Default,,0000,0000,0000,,or do I divide by 1,000?
Dialogue: 0,0:03:56.25,0:03:58.72,Default,,0000,0000,0000,,And you always have to say,\Nwell, if I'm going from
Dialogue: 0,0:03:58.72,0:04:03.05,Default,,0000,0000,0000,,kilometers to meters, I'm\Ngoing-- 1 kilometer is
Dialogue: 0,0:04:03.05,0:04:05.55,Default,,0000,0000,0000,,1,000 meters, right?
Dialogue: 0,0:04:05.55,0:04:07.82,Default,,0000,0000,0000,,So I'm going to be\Nmultiplying by 1,000.
Dialogue: 0,0:04:07.82,0:04:09.13,Default,,0000,0000,0000,,I'm going to get\Na bigger number.
Dialogue: 0,0:04:09.13,0:04:12.49,Default,,0000,0000,0000,,So that's why I went from\N0.05, and I multiplied it
Dialogue: 0,0:04:12.49,0:04:14.60,Default,,0000,0000,0000,,by 1,000, and I got 50.
Dialogue: 0,0:04:14.60,0:04:16.10,Default,,0000,0000,0000,,So let's get back\Nto the problem.
Dialogue: 0,0:04:16.10,0:04:19.40,Default,,0000,0000,0000,,0.05 kilometers is\Nequal to 50 meters.
Dialogue: 0,0:04:19.40,0:04:20.21,Default,,0000,0000,0000,,We're not done yet.
Dialogue: 0,0:04:20.21,0:04:23.28,Default,,0000,0000,0000,,Now, you need to convert those\N50 meters into centimeters.
Dialogue: 0,0:04:23.28,0:04:25.54,Default,,0000,0000,0000,,Well, we do the same thing.
Dialogue: 0,0:04:25.54,0:04:32.73,Default,,0000,0000,0000,,50 meters times-- how many-- so\Nwhat's the relationship between
Dialogue: 0,0:04:32.73,0:04:33.74,Default,,0000,0000,0000,,meters and centimeters?
Dialogue: 0,0:04:33.74,0:04:36.32,Default,,0000,0000,0000,,Well, if we look at the\Nchart, we see it's 100.
Dialogue: 0,0:04:36.32,0:04:38.31,Default,,0000,0000,0000,,And the question I'm going to\Nask you, am I going to multiply
Dialogue: 0,0:04:38.31,0:04:41.58,Default,,0000,0000,0000,,by 100, or am I going\Nto divide by 100?
Dialogue: 0,0:04:41.58,0:04:42.52,Default,,0000,0000,0000,,Well, it's the same thing.
Dialogue: 0,0:04:42.52,0:04:45.32,Default,,0000,0000,0000,,We're going from a bigger unit\Nto a smaller unit, so one of
Dialogue: 0,0:04:45.32,0:04:48.24,Default,,0000,0000,0000,,a bigger unit is equal to a\Nbunch of the smaller units.
Dialogue: 0,0:04:48.24,0:04:50.33,Default,,0000,0000,0000,,So we're going to multiply.
Dialogue: 0,0:04:50.33,0:04:56.59,Default,,0000,0000,0000,,So we say times 100\Ncentimeters per meter, right?
Dialogue: 0,0:04:56.59,0:04:57.33,Default,,0000,0000,0000,,And that just makes sense.
Dialogue: 0,0:04:57.33,0:04:59.71,Default,,0000,0000,0000,,There's 100 centimeters\Nper meter.
Dialogue: 0,0:04:59.71,0:05:02.84,Default,,0000,0000,0000,,So 50 meters times 100\Ncentimeters per meter is equal
Dialogue: 0,0:05:02.84,0:05:12.62,Default,,0000,0000,0000,,to 50 times 100 is 5,000, and\Nthen the meters cancel out,
Dialogue: 0,0:05:12.62,0:05:15.26,Default,,0000,0000,0000,,and you get centimeters.
Dialogue: 0,0:05:15.26,0:05:21.33,Default,,0000,0000,0000,,So what we have here is that\N0.05 kilometers is equal
Dialogue: 0,0:05:21.33,0:05:24.85,Default,,0000,0000,0000,,to 5,000 centimeters.
Dialogue: 0,0:05:24.85,0:05:26.09,Default,,0000,0000,0000,,Let's do another problem.
Dialogue: 0,0:05:26.09,0:05:28.58,Default,,0000,0000,0000,,I think the more examples\Nyou see, it'll make them
Dialogue: 0,0:05:28.58,0:05:28.94,Default,,0000,0000,0000,,a little more sense.
Dialogue: 0,0:05:28.94,0:05:31.36,Default,,0000,0000,0000,,And always try to visualize\Nwhat we're doing, the scale.
Dialogue: 0,0:05:31.36,0:05:32.83,Default,,0000,0000,0000,,Otherwise, it's very\Nconfusing whether you
Dialogue: 0,0:05:32.83,0:05:36.02,Default,,0000,0000,0000,,should multiply or divide.
Dialogue: 0,0:05:36.02,0:05:41.10,Default,,0000,0000,0000,,Let's say I have 422 decigrams.
Dialogue: 0,0:05:41.10,0:05:47.11,Default,,0000,0000,0000,,Grams are a measure of mass.
Dialogue: 0,0:05:49.53,0:05:51.47,Default,,0000,0000,0000,,One gram is actually\Na very small amount.
Dialogue: 0,0:05:51.47,0:05:53.71,Default,,0000,0000,0000,,That's what you measure--\NI guess in the metric
Dialogue: 0,0:05:53.71,0:05:56.77,Default,,0000,0000,0000,,system, they measure\Ngold in terms of grams.
Dialogue: 0,0:05:56.77,0:06:03.18,Default,,0000,0000,0000,,And I want to convert\Nthis into milligrams.
Dialogue: 0,0:06:03.18,0:06:07.20,Default,,0000,0000,0000,,So before we start the problem,\Nlet's just do a reality check.
Dialogue: 0,0:06:07.20,0:06:09.70,Default,,0000,0000,0000,,Am I going from a bigger unit\Nto a smaller unit, or a smaller
Dialogue: 0,0:06:09.70,0:06:10.87,Default,,0000,0000,0000,,unit to a bigger unit?
Dialogue: 0,0:06:10.87,0:06:18.87,Default,,0000,0000,0000,,Well, decigrams, that's 1/10\Nof a gram, and I'm going
Dialogue: 0,0:06:18.87,0:06:23.11,Default,,0000,0000,0000,,to 1/1,000 of a gram.
Dialogue: 0,0:06:23.11,0:06:25.75,Default,,0000,0000,0000,,\NSo there's two ways\Nof doing this.
Dialogue: 0,0:06:26.96,0:06:29.94,Default,,0000,0000,0000,,We can convert to grams and\Nthen convert to the other unit.
Dialogue: 0,0:06:29.94,0:06:32.35,Default,,0000,0000,0000,,That sometimes\Nmake things easy.
Dialogue: 0,0:06:32.35,0:06:35.91,Default,,0000,0000,0000,,Or we could say, well,\Nhow many milligrams is
Dialogue: 0,0:06:35.91,0:06:37.92,Default,,0000,0000,0000,,equal to one decigram?
Dialogue: 0,0:06:37.92,0:06:42.14,Default,,0000,0000,0000,,Well, a milligram, as\Nwe see here, is 100
Dialogue: 0,0:06:42.14,0:06:43.27,Default,,0000,0000,0000,,times smaller, right?
Dialogue: 0,0:06:43.27,0:06:47.33,Default,,0000,0000,0000,,To go from 1/10 to 1/1,000,\Nyou have to decrease
Dialogue: 0,0:06:47.33,0:06:48.78,Default,,0000,0000,0000,,in size by 100.
Dialogue: 0,0:06:48.78,0:07:02.57,Default,,0000,0000,0000,,So we could just say 422\Ndecigrams times 100
Dialogue: 0,0:07:02.57,0:07:08.23,Default,,0000,0000,0000,,milligrams per decigram.
Dialogue: 0,0:07:08.23,0:07:12.39,Default,,0000,0000,0000,,\NAnd then the decigrams will\Ncancel out, and I'll get 422
Dialogue: 0,0:07:17.62,0:07:24.40,Default,,0000,0000,0000,,times 100, 42,200 milligrams.
Dialogue: 0,0:07:24.40,0:07:29.95,Default,,0000,0000,0000,,\NNow, another way you could have\Ndone it is the way we just
Dialogue: 0,0:07:31.79,0:07:32.81,Default,,0000,0000,0000,,did that last problem.
Dialogue: 0,0:07:32.81,0:07:36.88,Default,,0000,0000,0000,,We could say 422 decigrams, we\Ncould convert that to grams.
Dialogue: 0,0:07:36.88,0:07:41.62,Default,,0000,0000,0000,,We could say 422-- I'm\Njust going to say dg.
Dialogue: 0,0:07:41.62,0:07:45.50,Default,,0000,0000,0000,,That's not really a\Nfamiliar unit-- decigrams.
Dialogue: 0,0:07:45.50,0:07:48.15,Default,,0000,0000,0000,,And how many decigrams\Nare there per gram?
Dialogue: 0,0:07:48.15,0:07:51.26,Default,,0000,0000,0000,,If we're going to gram, 422\Nis going to be a smaller
Dialogue: 0,0:07:51.26,0:07:53.36,Default,,0000,0000,0000,,number of grams, right?
Dialogue: 0,0:07:53.36,0:07:59.11,Default,,0000,0000,0000,,So we could say times\N1 decigram is equal
Dialogue: 0,0:07:59.11,0:08:01.23,Default,,0000,0000,0000,,to how many grams?
Dialogue: 0,0:08:01.23,0:08:07.20,Default,,0000,0000,0000,,Well, 1 decigram is\Nequal to-- no, sorry.
Dialogue: 0,0:08:07.20,0:08:09.80,Default,,0000,0000,0000,,1 gram is equal to\Nhow many decigrams?
Dialogue: 0,0:08:09.80,0:08:13.65,Default,,0000,0000,0000,,Well, 1 gram is equal\Nto 10 decigrams.
Dialogue: 0,0:08:13.65,0:08:16.56,Default,,0000,0000,0000,,And the reason why this makes\Nsense is if we have a decigram
Dialogue: 0,0:08:16.56,0:08:18.29,Default,,0000,0000,0000,,in the numerator here, we want\Na decigram in the
Dialogue: 0,0:08:18.29,0:08:19.79,Default,,0000,0000,0000,,denominator here.
Dialogue: 0,0:08:19.79,0:08:26.48,Default,,0000,0000,0000,,So if we have decigrams cancel\Nout, 422 decigrams will equal--
Dialogue: 0,0:08:26.48,0:08:33.24,Default,,0000,0000,0000,,that divided by 10 is\Nequal to 42.2 grams.
Dialogue: 0,0:08:33.24,0:08:35.77,Default,,0000,0000,0000,,And now we can just go\Nfrom grams to milligrams.
Dialogue: 0,0:08:35.77,0:08:37.12,Default,,0000,0000,0000,,Well, that's an easy one.
Dialogue: 0,0:08:37.12,0:08:41.15,Default,,0000,0000,0000,,1 gram is equal to 1,000\Nmilligrams, so we could say
Dialogue: 0,0:08:41.15,0:08:48.62,Default,,0000,0000,0000,,times 1,000 milligram per gram.
Dialogue: 0,0:08:48.62,0:08:53.68,Default,,0000,0000,0000,,The grams cancel out, and\Nwe're left with 42,200
Dialogue: 0,0:08:53.68,0:08:55.31,Default,,0000,0000,0000,,milligrams, right?
Dialogue: 0,0:08:55.31,0:08:59.38,Default,,0000,0000,0000,,42.2 times 1,000.
Dialogue: 0,0:08:59.38,0:09:01.53,Default,,0000,0000,0000,,Hopefully, that doesn't\Nconfuse you too much.
Dialogue: 0,0:09:01.53,0:09:04.33,Default,,0000,0000,0000,,The important thing is to\Nalways take a step back and
Dialogue: 0,0:09:04.33,0:09:06.96,Default,,0000,0000,0000,,really visualize and think\Nabout, should I be getting a
Dialogue: 0,0:09:06.96,0:09:09.31,Default,,0000,0000,0000,,larger number or a smaller\Nnumber than the one
Dialogue: 0,0:09:09.31,0:09:10.92,Default,,0000,0000,0000,,I started off with?
Dialogue: 0,0:09:10.92,0:09:13.84,Default,,0000,0000,0000,,I think you're ready to\Nnow try some problems.
Dialogue: 0,0:09:13.84,0:09:15.32,Default,,0000,0000,0000,,Have fun!