1 00:00:00,163 --> 00:00:02,208 Based on the examples in the last video 2 00:00:02,208 --> 00:00:07,764 let's see if we can come up with some rules of thumb for figuring out how many significant figures, 3 00:00:07,764 --> 00:00:08,957 or how many significant digits, 4 00:00:08,957 --> 00:00:11,912 there are in a number - or a measurement. 5 00:00:11,912 --> 00:00:16,834 So the first thing that is pretty obvious is that any non-zero digit, 6 00:00:16,834 --> 00:00:19,574 and any of the zero digits in between are significant. 7 00:00:19,574 --> 00:00:24,375 Really the 7 and the 5 here are significant and the zero's in between them, it's also going to be significant. 8 00:00:24,375 --> 00:00:37,763 So let's write this over here: so, any non-zero digits and zero's in between 9 00:00:37,763 --> 00:00:43,677 are going to be significant. That's pretty straightforward. 10 00:00:43,677 --> 00:00:49,436 Now the zero's that are not in between non-zero digits, these become a little bit more confusing. 11 00:00:49,436 --> 00:00:52,315 So let's just make sure we can rule out some of them. 12 00:00:52,315 --> 00:00:56,542 So you can always rule out - when you're thinking about significant figures - 13 00:00:56,542 --> 00:00:57,875 the leading zero's. 14 00:00:57,875 --> 00:01:00,169 And when I talk about leading zero's, I'm talking about the zero's 15 00:01:00,169 --> 00:01:03,507 that come before your non-zero digit. 16 00:01:03,507 --> 00:01:06,897 So these are leading zero's here, these are leading zero's. 17 00:01:06,897 --> 00:01:11,169 There's no leading zero's here, no leading zero's in this one, this one, and this one. 18 00:01:11,169 --> 00:01:15,349 But in any situation, the leading zero's are not significant. 19 00:01:15,349 --> 00:01:25,429 So leading zero's not significant. 20 00:01:25,429 --> 00:01:30,907 And so the last question, all you have left, I mean, you only have non-zero digits 21 00:01:30,907 --> 00:01:33,044 and zero's in between; you could have some leading zero's 22 00:01:33,044 --> 00:01:34,668 which you've already said are not significant. 23 00:01:34,668 --> 00:01:39,637 And so the only thing left that you have to figure out is what do you do with the trailing zero's, 24 00:01:39,637 --> 00:01:46,510 the zero's behind the last non-zero, or to the right of, the last non-zero digit. 25 00:01:46,510 --> 00:01:51,665 So that these trailing zero's here, there's actually two trailing zero's over, 26 00:01:51,665 --> 00:01:54,406 and then there is three trailing zero's over here. 27 00:01:54,406 --> 00:02:01,502 So let me make a little... so trailing zero's. 28 00:02:01,502 --> 00:02:02,669 What do we do with them? 29 00:02:02,669 --> 00:02:05,643 So the easy way to think about is, if you have a decimal, 30 00:02:05,643 --> 00:02:10,009 if there is a decimal anywhere in your number, count them. 31 00:02:10,009 --> 00:02:15,581 If you have a decimal count them as significant. 32 00:02:15,581 --> 00:02:20,597 they are significant. Count them as significant. 33 00:02:20,597 --> 00:02:25,659 If there is no decimal anywhere in the number, 34 00:02:25,659 --> 00:02:27,563 then it's kind of ambiguous. 35 00:02:27,563 --> 00:02:29,978 You're kind of not sure, and this is the situation. 36 00:02:29,978 --> 00:02:33,662 So clearly, over here, there's a decimal in the number 37 00:02:33,662 --> 00:02:37,269 so you count the trailing zeros - these are adding to the precision. 38 00:02:37,269 --> 00:02:40,984 Over here, there's a decimal so you count the trailing zero. 39 00:02:40,984 --> 00:02:43,260 There's a decimal here so you count the trailing zero's. 40 00:02:43,260 --> 00:02:45,349 There are no trailing zero's here. 41 00:02:45,349 --> 00:02:49,669 And over here, well the way I later put a decimal here, 42 00:02:49,669 --> 00:02:54,312 here you would count it, so if you have a decimal there you would count all five. 43 00:02:54,312 --> 00:02:59,978 If you didn't have the decimal, if you just had 37,000 like that 44 00:02:59,978 --> 00:03:04,343 it's ambiguous, and if someone doesn't give you more information 45 00:03:04,343 --> 00:03:08,987 you're best assumption is probably that they just measured to the nearest thousand, 46 00:03:08,987 --> 00:03:11,210 that they didn't measure exactly to the one and just happened 47 00:03:11,210 --> 00:03:13,586 to get exactly on 37,000. 48 00:03:13,586 --> 00:03:16,510 So if there's no decimal, let me write it this way, 49 00:03:16,510 --> 00:03:23,662 it's ambiguous, which means that you're really not sure what it means, 50 00:03:23,662 --> 00:03:27,333 it's not clear what it means, and you're proabably safer assuming 51 00:03:27,333 --> 00:03:35,644 to not count the trailing zero's. 52 00:03:35,644 --> 00:03:38,568 If someone really does measure, if you were to really measure something 53 00:03:38,568 --> 00:03:43,260 to the exact one, then you should put a decimal at the end like that. 54 00:03:43,260 --> 00:03:46,862 And there is a notation for specifying: 55 00:03:46,862 --> 00:03:49,669 let's say you do measure - let me do a different number - 56 00:03:49,669 --> 00:03:53,848 let's say you do measure 56,000 57 00:03:53,848 --> 00:03:59,003 and there is a notation for specifying that 6 definitely is the last significant digit 58 00:03:59,003 --> 00:04:01,975 and sometimes you'll see a bar put over the 6, 59 00:04:01,975 --> 00:04:04,576 sometimes you'll see a bar put under the 6. 60 00:04:04,576 --> 00:04:07,642 And that could be useful, because maybe, you're last 61 00:04:07,642 --> 00:04:09,671 significant digit is this zero over here, 62 00:04:09,671 --> 00:04:13,492 maybe you were able to measure to the 100's with a reasonable level of precision. 63 00:04:13,492 --> 00:04:16,511 And so then you would write something like, 64 00:04:16,511 --> 00:04:19,901 you'd still write 56,000, 65 00:04:19,901 --> 00:04:22,641 but then you would put the bar above that zero 66 00:04:22,641 --> 00:04:26,681 or the bar below that zero to say that that was the last significat digit. 67 00:04:26,681 --> 00:04:30,582 So if you saw something like this, you would say 3 significant digits. 68 00:04:30,582 --> 00:04:35,646 This isn't used so frequently. A better way to show that you've measured 69 00:04:35,646 --> 00:04:40,012 to 3 significant digits would be to write it in scientific notation. 70 00:04:40,012 --> 00:04:41,187 There's a whole video on that. 71 00:04:41,187 --> 00:04:43,167 But to write this in scientific notation, 72 00:04:43,167 --> 00:04:51,637 you could write this as 5.60 times 10 to the fourth power, right? 73 00:04:51,637 --> 00:04:55,335 Cause if you multiply this by 10 to the fourth 74 00:04:55,335 --> 00:04:57,054 you'd move this decimal over four spaces 75 00:04:57,054 --> 00:04:59,003 and get us to 56,000. 76 00:04:59,003 --> 00:05:02,000 So 5.60 times 10 to the fourth; 77 00:05:02,000 --> 00:05:03,124 and if this confuses you, 78 00:05:03,124 --> 00:05:05,319 watch the video on scientific notation. 79 00:05:05,319 --> 00:05:06,991 Hopefully it will clarify things a little bit. 80 00:05:06,991 --> 00:05:10,010 But when you write a number in scientific notation, 81 00:05:10,010 --> 00:05:12,426 it makes it very clear about your precision 82 00:05:12,426 --> 00:05:14,400 and how many significant digits you're dealing with. 83 00:05:14,400 --> 00:05:17,054 So instead of doing this notation that's a little bit outdated, 84 00:05:17,054 --> 00:05:18,601 I haven't seen it used much, 85 00:05:18,601 --> 00:05:21,666 with these bars below or above the high significant digit, 86 00:05:21,666 --> 00:05:23,988 instead you can represent it with a decimal 87 00:05:23,988 --> 00:05:26,018 in scientific notation 88 00:05:26,018 --> 00:05:31,000 and then it's very clear you have 3 significant digits. 89 00:05:31,000 --> 00:05:31,976 So hopefully that helps you out. 90 00:05:31,976 --> 00:05:33,133 In the next couple of videos, 91 00:05:33,133 --> 00:05:36,109 we'll explore a little bit more why significant digits are important 92 00:05:36,109 --> 99:59:59,999 especially when you do calculations with multiple measurements.