WEBVTT 00:00:00.200 --> 00:00:00.700 Welcome to the presentation on ordering numbers. 00:00:00.700 --> 00:00:06.940 Let's get started with some problems that I think, 00:00:06.940 --> 00:00:09.270 as you go through the examples, 00:00:09.270 --> 00:00:10.910 hopefully you'll understand how to do these problems. 00:00:10.910 --> 00:00:11.700 So let's see. 00:00:11.700 --> 00:00:23.200 The first set of numbers that we have to order is thirty-five point seven percent, 00:00:23.200 --> 00:00:44.590 one hundred eight point one percent, zero point five, thirteen over ninety-three, one, and seven over sixty-eight. 00:00:44.590 --> 00:00:46.590 So let's do this problem. 00:00:46.590 --> 00:00:48.810 The important thing to remember whenever you're doing this type of ordering of numbers 00:00:48.810 --> 00:00:52.820 is to realize that these are all just different ways to represent-- 00:00:52.820 --> 00:00:56.940 these are all a percent or a decimal or a fraction or a mixed-- 00:00:56.940 --> 00:01:00.270 are all just different ways of representing numbers. 00:01:02.680 --> 00:01:05.110 It's very hard to compare when you just look at it like this, 00:01:05.110 --> 00:01:07.130 so what I like to do is I like to convert them all to decimals. 00:01:08.190 --> 00:01:11.100 But there could be someone who likes to convert them all to percentages, 00:01:11.100 --> 00:01:14.220 or convert them all to fractions and then compare. 00:01:14.220 --> 00:01:16.920 But I always find decimals to be the easiest way to compare. 00:01:16.920 --> 00:01:19.370 So let's start with this thirty-five point seven percent. 00:01:19.370 --> 00:01:21.940 Let's turn this into a decimal. 00:01:21.940 --> 00:01:25.090 Well, the easiest thing to remember is if you have a percent, 00:01:25.090 --> 00:01:27.490 you just get rid of the percent sign and put it over one hundred. 00:01:28.580 --> 00:01:38.970 So thirty-five point seven percent is the same thing as thirty-five point seven over one hundred. 00:01:38.970 --> 00:01:43.020 Like five percent, that's the same thing as five over one hundred, 00:01:43.020 --> 00:01:45.050 or fifty percent is just the same thing as fifty over one hundred. 00:01:45.050 --> 00:01:53.990 So thirty-five point seven over one hundred, well, that just equals zero point three five seven. 00:01:53.990 --> 00:01:55.730 If this got you a little confused, 00:01:55.730 --> 00:02:01.970 another way to think about percentage points is if I write thirty-five point seven percent, 00:02:01.970 --> 00:02:05.540 all you have to do is get rid of the percent sign and move the decimal to the left two spaces, 00:02:05.540 --> 00:02:10.140 and it becomes zero point three five seven. 00:02:10.140 --> 00:02:11.870 Let me give you a couple of more examples down here. 00:02:11.870 --> 00:02:16.050 Let's say I had five percent. 00:02:16.050 --> 00:02:20.020 That is the same thing as five over one hundred. 00:02:20.020 --> 00:02:22.670 Or if you do the decimal technique, five percent, 00:02:22.670 --> 00:02:24.730 you could just move the decimal and you get rid of the percent. 00:02:24.730 --> 00:02:28.630 And you move the decimal over one and two, and you put a zero here. 00:02:28.630 --> 00:02:30.370 It's zero point zero five. 00:02:30.370 --> 00:02:33.280 And that's the same thing as zero point zero five. 00:02:33.280 --> 00:02:36.380 You also know that zero point zero five and five over one hundred are the same thing. 00:02:36.380 --> 00:02:37.620 So let's get back to the problem. 00:02:37.620 --> 00:02:40.772 I hope that distraction didn't distract you too much. 00:02:40.772 --> 00:02:43.190 Let me scratch out all this. 00:02:43.190 --> 00:02:49.050 So thirty-five point seven percent is equal to zero point three five seven. 00:02:49.050 --> 00:02:51.870 Similarly, one hundred eight point one percent-- 00:02:51.870 --> 00:02:54.080 Let's to the technique where we just get rid of the percent and 00:02:54.080 --> 00:02:59.350 move the decimal space over 1, 2 spaces to the left. 00:02:59.350 --> 00:03:08.600 So then that equals 1.081. 00:03:08.600 --> 00:03:11.570 See we already know that this is smaller than this. 00:03:11.570 --> 00:03:14.140 Well the next one is easy, it's already in decimal form. 00:03:14.140 --> 00:03:16.040 0.5 is just going to be equal to 0.5. 00:03:16.040 --> 00:03:18.820 Now 13/93. 00:03:21.050 --> 00:03:24.340 To convert a fraction into a decimal we just take the 00:03:24.340 --> 00:03:27.320 denominator and divide it into the numerator. 00:03:27.320 --> 00:03:29.350 So let's do that. 00:03:29.350 --> 00:03:33.020 93 goes into 13? 00:03:34.775 --> 00:03:36.530 Well, we know it goes into 13 zero times. 00:03:39.760 --> 00:03:43.990 So let's add a decimal point here. 00:03:43.990 --> 00:03:47.550 So how many times does 93 go into 130? 00:03:47.550 --> 00:03:49.530 Well, it goes into it one time. 00:03:49.530 --> 00:03:51.564 1 times 93 is 93. 00:03:55.364 --> 00:03:56.569 Becomes a 10. 00:03:56.673 --> 00:03:58.637 That becomes a 2. 00:03:58.960 --> 00:04:03.700 Then we're going to borrow, so get 37. 00:04:03.700 --> 00:04:06.590 Bring down a 0. 00:04:06.590 --> 00:04:10.010 So 93 goes into 370? 00:04:10.010 --> 00:04:10.470 Let's see. 00:04:10.470 --> 00:04:14.790 4 times 93 would be 372, so it actually goes into 00:04:14.790 --> 00:04:15.695 it only three times. 00:04:15.695 --> 00:04:19.390 3 times 3 is 9. 00:04:22.880 --> 00:04:25.270 3 times 9 is 27. 00:04:25.270 --> 00:04:30.110 So this equals? 00:04:31.605 --> 00:04:38.050 Let's see, this equals-- if we say that this 0 becomes a 10. 00:04:38.050 --> 00:04:39.620 This become a 16. 00:04:39.620 --> 00:04:42.440 This becomes a 2. 00:04:42.440 --> 00:04:45.210 81. 00:04:45.210 --> 00:04:48.120 And then we say, how many times does 93 go into 810? 00:04:48.120 --> 00:04:50.860 It goes roughly 8 times. 00:04:50.860 --> 00:04:52.860 And we could actually keep going, but for the sake of 00:04:52.860 --> 00:04:55.640 comparing these numbers, we've already gotten to a pretty 00:04:55.640 --> 00:04:57.580 good level of accuracy. 00:04:57.580 --> 00:05:00.740 So let's just stop this problem here because the decimal 00:05:00.740 --> 00:05:02.720 numbers could keep going on, but for the sake of comparison 00:05:02.720 --> 00:05:04.410 I think we've already got a good sense of what this 00:05:04.410 --> 00:05:05.360 decimal looks like. 00:05:05.360 --> 00:05:10.330 It's 0.138 and then it'll just keep going. 00:05:10.330 --> 00:05:13.010 So let's write that down. 00:05:13.010 --> 00:05:15.340 And then finally, we have this mixed number here. 00:05:15.340 --> 00:05:18.070 And let me erase some of my work because I don't 00:05:18.070 --> 00:05:18.840 want to confuse you. 00:05:18.840 --> 00:05:22.700 Actually, let me keep it the way it is right now. 00:05:22.700 --> 00:05:26.120 The easiest way to convert a mixed number into a decimal is 00:05:26.120 --> 00:05:29.630 to just say, OK, this is 1 and then some fraction 00:05:29.630 --> 00:05:32.920 that's less than 1. 00:05:32.920 --> 00:05:36.420 Or we could convert it to a fraction, an improper fraction 00:05:36.420 --> 00:05:38.790 like-- oh, actually there are no improper fractions here. 00:05:38.790 --> 00:05:39.640 Actually, let's do it that way. 00:05:39.640 --> 00:05:41.630 Let's convert to an improper fraction and then convert 00:05:41.630 --> 00:05:44.110 that into a decimal. 00:05:44.110 --> 00:05:46.060 Actually, I think I'm going to need more space, so let me 00:05:46.060 --> 00:05:48.740 clean up this a little bit. 00:05:48.740 --> 00:05:58.240 There. 00:05:58.595 --> 00:06:01.040 We have a little more space to work with now. 00:06:01.040 --> 00:06:04.260 So 1 and 7/68. 00:06:08.570 --> 00:06:13.700 So to go from a mixed number to an improper fraction, what you 00:06:13.700 --> 00:06:18.760 do is you take the 68 times 1 and add it to the 00:06:18.760 --> 00:06:19.720 numerator here. 00:06:26.120 --> 00:06:29.680 1 and 7/68 is the same thing as 1 plus 7/68. 00:06:29.680 --> 00:06:32.800 And that's the same thing as you know from the fractions 00:06:32.800 --> 00:06:40.330 module, as 68/68 plus 7/68. 00:06:40.330 --> 00:06:47.650 And that's the same thing as 68 plus 7-- 75/68. 00:06:47.650 --> 00:06:51.790 So 1 and 7/68 is equal to 75/68. 00:06:51.790 --> 00:06:54.870 And now we convert this to a decimal using the technique 00:06:54.870 --> 00:06:56.350 we did for 13/93. 00:06:56.350 --> 00:06:58.570 So we say-- let me get some space. 00:07:07.360 --> 00:07:09.160 68 goes into 75 one time. 00:07:09.160 --> 00:07:13.290 1 times 68 is 68. 00:07:13.290 --> 00:07:16.460 75 minus 68 is 7. 00:07:16.460 --> 00:07:17.350 Bring down the 0. 00:07:17.350 --> 00:07:20.490 Actually, you don't have to write the decimal there. 00:07:20.490 --> 00:07:21.100 Ignore that decimal. 00:07:21.100 --> 00:07:24.400 68 goes into 70 one time. 00:07:24.400 --> 00:07:28.150 1 times 68 is 68. 00:07:28.150 --> 00:07:30.990 70 minus 68 is 2, bring down another 0. 00:07:30.990 --> 00:07:33.240 68 goes into 20 zero times. 00:07:33.240 --> 00:07:36.550 And the problem's going to keep going on, but I think we've 00:07:36.550 --> 00:07:38.990 already once again, gotten to enough accuracy that 00:07:38.990 --> 00:07:40.040 we can compare. 00:07:40.040 --> 00:07:48.320 So 1 and 7/68 we've now figured out is equal to 1.10 -- and if we kept dividing we'd get more decimals of accuracy. So we're ready to compare. 00:07:53.510 --> 00:07:56.550 So all of these numbers I just rewrote them as decimals. 00:07:56.550 --> 00:08:00.550 So 35.7% is 0.357. 00:08:05.720 --> 00:08:09.660 It's 108.1% is equal to 1.081. 00:08:09.660 --> 00:08:11.260 0.5 is 0.5. 00:08:11.260 --> 00:08:15.770 13/93 is 0.138. 00:08:15.770 --> 00:08:20.850 And 1 and 7/68 is 1.10 and it'll keep going on. 00:08:20.850 --> 00:08:23.010 So what's the smallest? 00:08:23.010 --> 00:08:26.320 So the smallest is . -- actually, no. 00:08:26.320 --> 00:08:28.300 The smallest is right here. 00:08:28.300 --> 00:08:31.450 So I'm going to rank them from smallest to largest. 00:08:31.450 --> 00:08:36.250 So the smallest is 0.138. 00:08:36.250 --> 00:08:40.640 Then the next largest is going to be 0.357. Right? 00:08:40.640 --> 00:08:44.470 Then the next largest is going to be 0.5. 00:08:44.470 --> 00:08:47.460 Then you're going to have 1.08. 00:08:47.460 --> 00:08:54.620 And then you're going to have 1 and 7/68. 00:08:54.620 --> 00:08:56.840 Well, actually, I'm going to do more examples of this, but for 00:08:56.840 --> 00:08:59.890 this video I think this is the only one I have time for. 00:08:59.890 --> 00:09:01.910 But hopefully this gives you a sense of doing these problems. 00:09:01.910 --> 00:09:04.370 I always find it easier to go into the decimal 00:09:04.370 --> 00:09:05.280 mode to compare. 00:09:05.280 --> 00:09:06.680 And actually, the hints on the module will 00:09:06.680 --> 00:09:08.670 be the same for you. 00:09:08.670 --> 00:09:11.040 But I think you're ready at least now to try the problems. 00:09:11.040 --> 00:09:13.170 If you're not, if you want to see other examples, you might 00:09:13.170 --> 00:09:16.830 just want to either re-watch this video and/or I might 00:09:16.830 --> 00:09:20.530 record some more videos with more examples right now. 00:09:20.530 --> 00:09:22.560 Anyway, have fun.