2 00:00:11,237 --> 00:00:14,372 One of the most useful skills that you 3 00:00:14,372 --> 00:00:21,100 can pick up, in scientific quantitative analysis, 4 00:00:21,100 --> 00:00:26,100 Is the ability to look at and manipulate 5 00:00:26,100 --> 00:00:28,550 the units that are attached to the numbers. 6 00:00:29,690 --> 00:00:32,150 This is called the factor-label method. 7 00:00:32,150 --> 00:00:36,330 And once you get it, it seems very intuitive, but it seems to me 8 00:00:36,330 --> 00:00:38,640 that nobody is born knowing how to do this, so you 9 00:00:38,640 --> 00:00:40,629 might have to work at it a little bit to get it. 10 00:00:42,740 --> 00:00:49,510 Say we have a number which is a velocity in units of kilometers per hour. 11 00:00:49,510 --> 00:00:54,960 And then we want to convert that into different units of meters per second. 12 00:00:54,960 --> 00:00:57,680 Instead of trying to remember a formula to do that, we 13 00:00:57,680 --> 00:01:01,660 can actually use the kilometers and the hours, meters, and seconds. 14 00:01:01,660 --> 00:01:08,388 To construct the formula that we need to do the conversion such 15 00:01:08,388 --> 00:01:10,780 that it will make the units work. 16 00:01:11,900 --> 00:01:15,520 So we'll start with a velocity in kilometers 17 00:01:15,520 --> 00:01:17,440 per hour, say we're driving along and it's 18 00:01:17,440 --> 00:01:20,529 100 kilometers per hour, and you want to know how many meters per second that is. 19 00:01:22,470 --> 00:01:25,550 So, we need to find factors that can 20 00:01:25,550 --> 00:01:29,280 convert these units into the ones that we want. 21 00:01:30,350 --> 00:01:34,580 And so let's start with the time units. 22 00:01:34,580 --> 00:01:41,020 We want to convert from hours to seconds. And so we'll start by writing a factor 23 00:01:41,020 --> 00:01:46,540 which can cancel out the units of hours here, and give us something shorter. 24 00:01:46,540 --> 00:01:48,480 And I don't remember in my head how many seconds 25 00:01:48,480 --> 00:01:50,210 there are in an hour, so I'll write it out. 26 00:01:51,410 --> 00:01:55,690 Do this in two stages, that there are 60 minutes 27 00:01:55,690 --> 00:01:59,710 in an hour, and so now we can cancel the 28 00:01:59,710 --> 00:02:05,750 units of hours here and that's the first step in our 29 00:02:07,030 --> 00:02:13,160 our factor label method. Now because an hour equals 60 minutes. 30 00:02:13,160 --> 00:02:17,820 If you take a quantity which is the same on the top and the 31 00:02:17,820 --> 00:02:23,220 bottom of a fraction, then that quotient is equal to one. 32 00:02:23,220 --> 00:02:24,950 So by multiplying our 33 00:02:24,950 --> 00:02:27,140 original information, which is 100 kilometers 34 00:02:27,140 --> 00:02:30,910 per hour, by this conversion factor, we're 35 00:02:30,910 --> 00:02:35,000 just multiplying by one, and so we're not actually changing the value at all. 36 00:02:35,000 --> 00:02:37,050 We're changing the units and so that changes 37 00:02:37,050 --> 00:02:39,490 the numbers, but the actual quantity stays the same. 38 00:02:41,080 --> 00:02:45,260 So the next factor will be from minutes 39 00:02:45,260 --> 00:02:48,520 to seconds, where 60 seconds equals one minute. 41 00:02:50,020 --> 00:02:55,130 Now the minute units are gone away and we have kilometers per second, 42 00:02:55,130 --> 00:02:58,990 so that's getting closer, but now we have to deal with the kilometers to meters. 43 00:02:58,990 --> 00:03:06,560 And so the conversion factor here is a kilometer is equal to 100 meters. 44 00:03:06,560 --> 00:03:08,260 And I have to put the kilometer on the bottom 45 00:03:08,260 --> 00:03:11,630 I can see, because I have to cancel kilometer here. 46 00:03:11,630 --> 00:03:14,110 And end up with meters on the top. 47 00:03:15,180 --> 00:03:19,028 So after we have constructed this whole thing to cancel out the units. 48 00:03:19,028 --> 00:03:21,230 It's meters. 49 00:03:21,230 --> 00:03:24,090 So we're left with what we want, meters per second. 50 00:03:24,090 --> 00:03:26,550 all we have to do is multiply the numbers. 51 00:03:26,550 --> 00:03:34,050 100 times 1000 divided by 60 divided by 60 gives us this answer. 52 00:03:34,050 --> 00:03:38,124 And so the units have told us how to do the math.