1 00:00:00,000 --> 00:00:00,910 2 00:00:00,910 --> 00:00:04,360 Welcome to the presentation on ordering numbers. 3 00:00:04,360 --> 00:00:06,940 Let's get started with some problems that I think, as you 4 00:00:06,940 --> 00:00:09,269 go through the examples hopefully, you'll understand 5 00:00:09,269 --> 00:00:10,910 how to do these problems. 6 00:00:10,910 --> 00:00:11,699 So let's see. 7 00:00:11,699 --> 00:00:23,199 The first set of numbers that we have to order is 35.7%, 8 00:00:23,199 --> 00:00:44,590 108.1% 0.5, 13/93, and 1 and 7/68. 9 00:00:44,590 --> 00:00:46,590 So let's do this problem. 10 00:00:46,590 --> 00:00:48,810 The important thing to remember whenever you're doing this type 11 00:00:48,810 --> 00:00:52,820 of ordering of numbers is to realize that these are all just 12 00:00:52,820 --> 00:00:56,939 different ways to represent-- these are all a percent or a 13 00:00:56,939 --> 00:01:00,269 decimal or a fraction or a mixed-- are all just different 14 00:01:00,270 --> 00:01:02,680 ways of representing numbers. 15 00:01:02,679 --> 00:01:05,109 It's very hard to compare when you just look at it like this, 16 00:01:05,109 --> 00:01:07,129 so what I like to do is I like to convert them 17 00:01:07,129 --> 00:01:08,189 all to decimals. 18 00:01:08,189 --> 00:01:11,099 But there could be someone who likes to convert them all to 19 00:01:11,099 --> 00:01:14,219 percentages or convert them all to fractions and then compare. 20 00:01:14,219 --> 00:01:16,920 But I always find decimals to be the easiest way to compare. 21 00:01:16,920 --> 00:01:19,370 So let's start with this 35.7%. 22 00:01:19,370 --> 00:01:21,939 Let's turn this into a decimal. 23 00:01:21,939 --> 00:01:25,090 Well, the easiest thing to remember is if you have a 24 00:01:25,090 --> 00:01:27,490 percent you just get rid of the percent sign and 25 00:01:27,489 --> 00:01:28,579 put it over 100. 26 00:01:28,579 --> 00:01:38,969 So 35.7% is the same thing as 35.7/100. 27 00:01:38,969 --> 00:01:43,019 Like 5%, that's the same thing as 5/100 or 50% is just 28 00:01:43,019 --> 00:01:45,049 the same thing as 50/100. 29 00:01:45,049 --> 00:01:53,989 So 35.7/100, well, that just equals 0.357. 30 00:01:53,989 --> 00:01:55,729 If this got you a little confused another way to think 31 00:01:55,730 --> 00:02:01,969 about percentage points is if I write 35.7%, all you have to do 32 00:02:01,969 --> 00:02:05,539 is get rid of the percent sign and move the decimal to the 33 00:02:05,540 --> 00:02:10,140 left two spaces and it becomes 0.357. 34 00:02:10,139 --> 00:02:11,869 Let me give you a couple of more examples down here. 35 00:02:11,870 --> 00:02:16,050 Let's say I had 5%. 36 00:02:16,050 --> 00:02:20,020 That is the same thing as 5/100. 37 00:02:20,020 --> 00:02:22,670 Or if you do the decimal technique, 5%, you could just 38 00:02:22,669 --> 00:02:24,729 move the decimal and you get rid of the percent. 39 00:02:24,729 --> 00:02:28,629 And you move the decimal over 1 and 2, and you put a 0 here. 40 00:02:28,629 --> 00:02:30,370 It's 0.05. 41 00:02:30,370 --> 00:02:33,280 And that's the same thing as 0.05. 42 00:02:33,280 --> 00:02:36,379 You also know that 0.05 and 5/100 are the same thing. 43 00:02:36,379 --> 00:02:37,620 So let's get back to the problem. 44 00:02:37,620 --> 00:02:40,771 I hope that distraction didn't distract you too much. 45 00:02:40,771 --> 00:02:43,189 Let me scratch out all this. 46 00:02:43,189 --> 00:02:49,050 So 35.7% is equal to 0.357. 47 00:02:49,050 --> 00:02:51,870 Similarly, 108.1%. 48 00:02:51,870 --> 00:02:54,080 Let's to the technique where we just get rid of the percent and 49 00:02:54,080 --> 00:02:59,350 move the decimal space over 1, 2 spaces to the left. 50 00:02:59,349 --> 00:03:08,599 So then that equals 1.081. 51 00:03:08,599 --> 00:03:11,569 See we already know that this is smaller than this. 52 00:03:11,569 --> 00:03:14,139 Well the next one is easy, it's already in decimal form. 53 00:03:14,139 --> 00:03:16,039 0.5 is just going to be equal to 0.5. 54 00:03:16,039 --> 00:03:18,819 55 00:03:18,819 --> 00:03:21,049 Now 13/93. 56 00:03:21,050 --> 00:03:24,340 To convert a fraction into a decimal we just take the 57 00:03:24,340 --> 00:03:27,319 denominator and divide it into the numerator. 58 00:03:27,319 --> 00:03:29,349 So let's do that. 59 00:03:29,349 --> 00:03:33,019 93 goes into 13? 60 00:03:33,020 --> 00:03:36,530 61 00:03:36,530 --> 00:03:39,759 Well, we know it goes into 13 zero times. 62 00:03:39,759 --> 00:03:43,989 So let's add a decimal point here. 63 00:03:43,990 --> 00:03:47,550 So how many times does 93 go into 130? 64 00:03:47,550 --> 00:03:49,530 Well, it goes into it one time. 65 00:03:49,530 --> 00:03:51,409 1 times 93 is 93. 66 00:03:51,409 --> 00:03:55,061 67 00:03:55,061 --> 00:03:56,550 Becomes a 10. 68 00:03:56,550 --> 00:03:58,960 That becomes a 2. 69 00:03:58,960 --> 00:04:03,700 Then we're going to borrow, so get 37. 70 00:04:03,699 --> 00:04:06,589 Bring down a 0. 71 00:04:06,590 --> 00:04:10,009 So 93 goes into 370? 72 00:04:10,009 --> 00:04:10,469 Let's see. 73 00:04:10,469 --> 00:04:14,789 4 times 93 would be 372, so it actually goes into 74 00:04:14,789 --> 00:04:15,694 it only three times. 75 00:04:15,694 --> 00:04:19,389 76 00:04:19,389 --> 00:04:22,879 3 times 3 is 9. 77 00:04:22,879 --> 00:04:25,269 3 times 9 is 27. 78 00:04:25,269 --> 00:04:30,109 79 00:04:30,110 --> 00:04:31,605 So this equals? 80 00:04:31,605 --> 00:04:38,050 Let's see, this equals-- if we say that this 0 becomes a 10. 81 00:04:38,050 --> 00:04:39,620 This become a 16. 82 00:04:39,620 --> 00:04:42,439 This becomes a 2. 83 00:04:42,439 --> 00:04:45,209 81. 84 00:04:45,209 --> 00:04:48,120 And then we say, how many times does 93 go into 810? 85 00:04:48,120 --> 00:04:50,860 It goes roughly 8 times. 86 00:04:50,860 --> 00:04:52,860 And we could actually keep going, but for the sake of 87 00:04:52,860 --> 00:04:55,639 comparing these numbers, we've already gotten to a pretty 88 00:04:55,639 --> 00:04:57,579 good level of accuracy. 89 00:04:57,579 --> 00:05:00,740 So let's just stop this problem here because the decimal 90 00:05:00,740 --> 00:05:02,720 numbers could keep going on, but for the sake of comparison 91 00:05:02,720 --> 00:05:04,410 I think we've already got a good sense of what this 92 00:05:04,410 --> 00:05:05,360 decimal looks like. 93 00:05:05,360 --> 00:05:10,330 It's 0.138 and then it'll just keep going. 94 00:05:10,329 --> 00:05:13,009 So let's write that down. 95 00:05:13,009 --> 00:05:15,339 And then finally, we have this mixed number here. 96 00:05:15,339 --> 00:05:18,069 And let me erase some of my work because I don't 97 00:05:18,069 --> 00:05:18,839 want to confuse you. 98 00:05:18,839 --> 00:05:22,699 Actually, let me keep it the way it is right now. 99 00:05:22,699 --> 00:05:26,120 The easiest way to convert a mixed number into a decimal is 100 00:05:26,120 --> 00:05:29,629 to just say, OK, this is 1 and then some fraction 101 00:05:29,629 --> 00:05:32,920 that's less than 1. 102 00:05:32,920 --> 00:05:36,420 Or we could convert it to a fraction, an improper fraction 103 00:05:36,420 --> 00:05:38,790 like-- oh, actually there are no improper fractions here. 104 00:05:38,790 --> 00:05:39,640 Actually, let's do it that way. 105 00:05:39,639 --> 00:05:41,629 Let's convert to an improper fraction and then convert 106 00:05:41,629 --> 00:05:44,110 that into a decimal. 107 00:05:44,110 --> 00:05:46,060 Actually, I think I'm going to need more space, so let me 108 00:05:46,060 --> 00:05:48,740 clean up this a little bit. 109 00:05:48,740 --> 00:05:58,240 110 00:05:58,240 --> 00:05:58,595 There. 111 00:05:58,595 --> 00:06:01,040 We have a little more space to work with now. 112 00:06:01,040 --> 00:06:04,260 113 00:06:04,259 --> 00:06:08,569 So 1 and 7/68. 114 00:06:08,569 --> 00:06:13,699 So to go from a mixed number to an improper fraction, what you 115 00:06:13,699 --> 00:06:18,759 do is you take the 68 times 1 and add it to the 116 00:06:18,759 --> 00:06:19,719 numerator here. 117 00:06:19,720 --> 00:06:21,000 And why does this make sense? 118 00:06:21,000 --> 00:06:26,120 Because this is the same thing as 1 plus 7/68. 119 00:06:26,120 --> 00:06:29,680 1 and 7/68 is the same thing as 1 plus 7/68. 120 00:06:29,680 --> 00:06:32,800 And that's the same thing as you know from the fractions 121 00:06:32,800 --> 00:06:40,329 module, as 68/68 plus 7/68. 122 00:06:40,329 --> 00:06:47,649 And that's the same thing as 68 plus 7-- 75/68. 123 00:06:47,649 --> 00:06:51,789 So 1 and 7/68 is equal to 75/68. 124 00:06:51,790 --> 00:06:54,870 And now we convert this to a decimal using the technique 125 00:06:54,870 --> 00:06:56,350 we did for 13/93. 126 00:06:56,350 --> 00:06:58,570 So we say-- let me get some space. 127 00:06:58,569 --> 00:07:05,000 We say 68 goes into 75-- suspicion I'm going 128 00:07:05,000 --> 00:07:07,360 to run out of space. 129 00:07:07,360 --> 00:07:09,160 68 goes into 75 one time. 130 00:07:09,160 --> 00:07:13,290 1 times 68 is 68. 131 00:07:13,290 --> 00:07:16,460 75 minus 68 is 7. 132 00:07:16,459 --> 00:07:17,349 Bring down the 0. 133 00:07:17,350 --> 00:07:20,490 Actually, you don't have to write the decimal there. 134 00:07:20,490 --> 00:07:21,100 Ignore that decimal. 135 00:07:21,100 --> 00:07:24,400 68 goes into 70 one time. 136 00:07:24,399 --> 00:07:28,149 1 times 68 is 68. 137 00:07:28,149 --> 00:07:30,989 70 minus 68 is 2, bring down another 0. 138 00:07:30,990 --> 00:07:33,240 68 goes into 20 zero times. 139 00:07:33,240 --> 00:07:36,550 And the problem's going to keep going on, but I think we've 140 00:07:36,550 --> 00:07:38,990 already once again, gotten to enough accuracy that 141 00:07:38,990 --> 00:07:40,040 we can compare. 142 00:07:40,040 --> 00:07:48,319 So 1 and 7/68 we've now figured out is equal to 1.10-- and if 143 00:07:48,319 --> 00:07:51,000 we kept dividing we'll keep getting more decimals of 144 00:07:51,000 --> 00:07:53,509 accuracy, but I think we're now ready to compare. 145 00:07:53,509 --> 00:07:56,550 So all of these numbers I just rewrote them as decimals. 146 00:07:56,550 --> 00:08:00,550 So 35.7% is 0.357. 147 00:08:00,550 --> 00:08:05,000 108.1%-- ignore this for now because we just used 148 00:08:05,000 --> 00:08:05,720 that to do the work. 149 00:08:05,720 --> 00:08:09,660 It's 108.1% is equal to 1.081. 150 00:08:09,660 --> 00:08:11,260 0.5 is 0.5. 151 00:08:11,259 --> 00:08:15,769 13/93 is 0.138. 152 00:08:15,769 --> 00:08:20,849 And 1 and 7/68 is 1.10 and it'll keep going on. 153 00:08:20,850 --> 00:08:23,010 So what's the smallest? 154 00:08:23,009 --> 00:08:26,319 So the smallest is 0.-- actually, no. 155 00:08:26,319 --> 00:08:28,300 The smallest is right here. 156 00:08:28,300 --> 00:08:31,449 So I'm going to rank them from smallest to largest. 157 00:08:31,449 --> 00:08:36,250 So the smallest is 0.138. 158 00:08:36,250 --> 00:08:40,639 Then the next largest is going to be 0.357. 159 00:08:40,639 --> 00:08:44,470 Then the next largest is going to be 0.5. 160 00:08:44,470 --> 00:08:47,460 Then you're going to have 1.08. 161 00:08:47,460 --> 00:08:54,620 And then you're going to have 1 and 7/68. 162 00:08:54,620 --> 00:08:56,840 Well, actually, I'm going to do more examples of this, but for 163 00:08:56,840 --> 00:08:59,889 this video I think this is the only one I have time for. 164 00:08:59,889 --> 00:09:01,909 But hopefully this gives you a sense of doing these problems. 165 00:09:01,909 --> 00:09:04,370 I always find it easier to go into the decimal 166 00:09:04,370 --> 00:09:05,279 mode to compare. 167 00:09:05,279 --> 00:09:06,679 And actually, the hints on the module will 168 00:09:06,679 --> 00:09:08,669 be the same for you. 169 00:09:08,669 --> 00:09:11,039 But I think you're ready at least now to try the problems. 170 00:09:11,039 --> 00:09:13,169 If you're not, if you want to see other examples, you might 171 00:09:13,169 --> 00:09:16,829 just want to either re-watch this video and/or I might 172 00:09:16,830 --> 00:09:20,530 record some more videos with more examples right now. 173 00:09:20,529 --> 00:09:22,559 Anyway, have fun.