﻿[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 ways of representing numbers. Dialogue: 0,0:01:02.12,0:01:04.87,Default,,0000,0000,0000,,It's very hared to compare when you just look at it like this,\N Dialogue: 0,0:01:04.90,0:01:07.47,Default,,0000,0000,0000,,so what I like to do is I like to convert them all to decimals. Dialogue: 0,0:01:07.49,0:01:11.67,Default,,0000,0000,0000,,But, you know,there could be someone who likes 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 the 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 if 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 and 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 if I write 35.7%, \N 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 more 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 and 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, and 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 5/100 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 we 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 1,2 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, it'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 and 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 that 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 does 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 pretty 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 sense 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 mixed 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, an improper fraction\N Dialogue: 0,0:05:36.43,0:05:38.79,Default,,0000,0000,0000,,like--oh, actually there are no 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 an 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 getting 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 rewrote 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 do 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 is 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 sense 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 the 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 will 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 now 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 eithere 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 with more examples right now. Dialogue: 0,0:09:19.86,9:59:59.99,Default,,0000,0000,0000,,Anyway, have fun.