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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:00,160 --> 00:00:02,840 Hey it’s Professor Dave; let’s work with percentages. 2 00:00:09,720 --> 00:00:14,860 We are all aware of percentages, as they are ubiquitous in society. 3 00:00:14,860 --> 00:00:17,470 There is a sale today, thirty percent off. 4 00:00:17,470 --> 00:00:20,350 Leave a twenty percent tip after the meal. 5 00:00:20,350 --> 00:00:23,650 Today there is a fifty percent chance of rain. 6 00:00:23,650 --> 00:00:25,300 So what are these things? 7 00:00:25,300 --> 00:00:31,190 Well in Latin, centum means one hundred, so percent literally means out of a hundred. 8 00:00:31,190 --> 00:00:37,440 It’s just a way of conveying magnitude, by modifying some total into a hundred, and 9 00:00:37,440 --> 00:00:42,550 then reporting a value of interest as some fraction of that hundred. 10 00:00:42,550 --> 00:00:49,530 If you get a ninety percent on your math quiz, you could have gotten nine points out of ten, 11 00:00:49,530 --> 00:00:54,719 eighteen points out of twenty, four hundred fifty out of five hundred, or any other number 12 00:00:54,719 --> 00:00:58,629 that obeys this ratio of ninety out of a hundred. 13 00:00:58,629 --> 00:01:03,600 Whatever we have to do to the larger number to make it one hundred, we do that same thing 14 00:01:03,600 --> 00:01:05,600 to the other number. 15 00:01:05,600 --> 00:01:12,580 Ten must be multiplied by ten to get a hundred, so the nine is also multiplied by ten. 16 00:01:12,580 --> 00:01:19,100 In this way, percentages are ratios, they are just very specific ratios that compare 17 00:01:19,100 --> 00:01:24,909 numbers to a hundred, because although this number is totally arbitrary, it is an ideal 18 00:01:24,909 --> 00:01:27,359 size for comparison. 19 00:01:27,359 --> 00:01:33,760 One hundred is small enough that our brains can easily comprehend its magnitude, but also 20 00:01:33,760 --> 00:01:40,640 large enough that there are sufficient gradations between zero and a hundred so as to make meaningful 21 00:01:40,640 --> 00:01:42,340 comparisons. 22 00:01:42,340 --> 00:01:47,549 In this way, we can look at percentages as simple fractions. 23 00:01:47,549 --> 00:01:50,850 Eighty percent is eighty one-hundredths. 24 00:01:50,850 --> 00:01:55,939 We learned how to simplify fractions, so let’s divide both of these numbers by twenty. 25 00:01:55,939 --> 00:01:58,530 We should get four fifths. 26 00:01:58,530 --> 00:02:05,009 This means that eighty percent and four fifths are equivalent; they mean the same thing. 27 00:02:05,009 --> 00:02:10,788 Moving to another example, fifty percent is fifty one hundredths, and dividing both numbers 28 00:02:10,788 --> 00:02:13,980 by fifty, we get one half. 29 00:02:13,980 --> 00:02:17,599 This makes sense, as fifty is half of a hundred. 30 00:02:17,599 --> 00:02:22,739 If you have something like three percent, that will be three one hundredths, and that 31 00:02:22,739 --> 00:02:25,930 can’t be simplified any further. 32 00:02:25,930 --> 00:02:32,319 We should be able to convert between percentages, fractions, and even decimals in this way with 33 00:02:32,320 --> 00:02:35,020 relative ease, so let’s check comprehension. 3209