1 00:00:00,453 --> 00:00:01,887 Now that we have a decent understanding of 2 00:00:01,887 --> 00:00:05,095 how to figure out many significant figures that we are dealing with 3 00:00:05,095 --> 00:00:07,862 lets take a situation where, 4 00:00:07,862 --> 00:00:11,881 significant figures will or might become relevant. 5 00:00:11,881 --> 00:00:14,482 So let's say that I have a carpet here 6 00:00:14,482 --> 00:00:21,100 and I'm using a may be a meter stick to measure the carpet to nearest centimeter. 7 00:00:21,100 --> 00:00:28,726 And so I get the carpet as on to the the nearest centimeter I get to be 1.69 meters. 8 00:00:28,726 --> 00:00:32,623 So this is 9, obiviously this is to the nearest centimeter. 9 00:00:32,623 --> 00:00:37,555 This 9 hundredths of a meter as the same thing as 9 centimeters. 10 00:00:37,555 --> 00:00:44,738 And let's say I'm able to measure the width here as 2.09 meters. 11 00:00:44,738 --> 00:00:47,457 I use the same meter stick and you were to ask me: 12 00:00:47,457 --> 00:00:50,951 "Sal, what is the area of your carpet?" 13 00:00:50,951 --> 00:00:53,380 So - you know - just to the straight up calculation: 14 00:00:53,380 --> 00:00:56,219 the area is going to be the length times the width, 15 00:00:56,219 --> 00:01:03,799 so it would be 1.69 meters times 2.09 meters. 16 00:01:03,799 --> 00:01:07,681 We could do this by hand, but let me just get the calculator out 17 00:01:07,681 --> 00:01:11,470 to make things move along a little bit faster. 18 00:01:11,470 --> 00:01:21,354 And so we have 1.69 times 2.09 and they gives us 3.5321. 19 00:01:21,354 --> 00:01:26,964 Let me write that down 3.5321. 20 00:01:26,964 --> 00:01:32,881 So let me write this in a new color. So this gives us 3.5321, 21 00:01:32,881 --> 00:01:37,548 and we have a meters times a meters which gives us meters squared or square meters. 22 00:01:37,548 --> 00:01:39,861 I might very proudly to tell you that 23 00:01:39,861 --> 00:01:44,581 "Hey the area is 3.5321 square meters. 24 00:01:44,581 --> 00:01:49,160 And the problem here is that it when I give you this thing 25 00:01:49,160 --> 00:01:51,744 that has all of these numbers behind the decimal point 26 00:01:51,744 --> 00:01:53,833 and all of these are significant figures 27 00:01:53,833 --> 00:01:58,828 that implies that I had a really precise way of measuring the area. 28 00:01:58,828 --> 00:02:03,979 But in reality I only was able to measure the area to the nearest centimeter. 29 00:02:03,979 --> 00:02:06,289 So the way we would do this we don't... 30 00:02:06,289 --> 00:02:10,215 so I don't make it look like my measurement is more precise than it really is. 31 00:02:10,215 --> 00:02:13,258 So this calculation is derived from my measurements. 32 00:02:13,258 --> 00:02:20,023 I make sure that it has no more significant figures then either of the numbers that I multiplied. 33 00:02:20,023 --> 00:02:25,651 So in this situation I have 3 significant figures here, 34 00:02:25,651 --> 00:02:31,276 and over here I have 3 significant figures. 35 00:02:31,276 --> 00:02:36,315 And so in general you multiply or devide the significant figures in your product 36 00:02:36,315 --> 00:02:50,215 or the divisor, divident, the quotient , the quotient! 37 00:02:50,215 --> 00:02:57,120 The numbers, the significant figures in your product or your quotient can not be any more than 38 00:02:57,120 --> 00:02:58,467 the least number of significant digits, 39 00:02:58,467 --> 00:03:01,067 or whatever you are using to come up with that product quotient. 40 00:03:01,067 --> 00:03:04,297 So over here both of these have 3 significant figures. 41 00:03:04,297 --> 00:03:08,605 So I can only have 3 significant figures in my product. 42 00:03:08,605 --> 00:03:12,697 If one of these had 3 significant figures and this have 2 significant figures, 43 00:03:12,697 --> 00:03:15,459 I can have only have 2 significant figures in my product. 44 00:03:15,459 --> 00:03:18,308 So in order to be kind of legit here, 45 00:03:18,308 --> 00:03:21,302 I have to round this to 3 significant figures. 46 00:03:21,302 --> 00:03:23,506 I have to round it to 3 significant figures, 47 00:03:23,506 --> 00:03:27,436 I need to round it to the nearest hundredth here 48 00:03:27,436 --> 00:03:30,969 and so this 2 will round down, so we got 49 00:03:30,969 --> 00:03:38,705 this gets us to 3.53 meters squared. 50 00:03:38,705 --> 00:03:41,044 Now we're cool with the significant figures. 51 00:03:41,044 --> 00:03:44,500 Let's do another situation with division! 52 00:03:44,500 --> 00:03:45,574 Let's say that I'm... 53 00:03:45,574 --> 00:03:48,767 Let's say that I'm laying tiles down in my bathroom, 54 00:03:48,767 --> 00:03:50,569 and so the diagram will look very similar, 55 00:03:50,569 --> 00:03:55,505 and I measure... I measure the... 56 00:03:55,505 --> 00:04:00,636 I measure the width of my bathroom to be, 57 00:04:00,636 --> 00:04:09,108 let's say it is 10.1 feet now. 10.1 feet. 58 00:04:09,108 --> 00:04:11,544 And this is the precision that I'm able to measure. 59 00:04:11,544 --> 00:04:14,302 So I'm able to measure the 10th of a foot. 60 00:04:14,302 --> 00:04:19,700 And let's say that the length of my floor is ... 61 00:04:19,700 --> 00:04:26,103 The length of my floor - I just make up a number - is 12 point... 62 00:04:26,103 --> 00:04:30,038 And for whatever reason I was able to measure this with slightly higher precision 63 00:04:30,038 --> 00:04:34,701 So 12.07 feet. And let's say... 64 00:04:34,701 --> 00:04:39,237 Let's say that I have tiles... I have tiles. 65 00:04:39,237 --> 00:04:46,836 And the tile has an area, so someone else measure for me, it has an area of... 66 00:04:46,836 --> 00:04:54,970 Let's say that the area of this tile is 1.07 feet squared. 67 00:04:54,970 --> 00:05:02,872 What I want to do is to figure out how many tiles can fit on this bathroom floor. 68 00:05:02,872 --> 00:05:07,452 So what I would do I would figure out the area of this bathroom floor, 69 00:05:07,452 --> 00:05:10,242 and then divide by the area of the tiles. 70 00:05:10,242 --> 00:05:14,454 So the area of the bathroom floor, so floor area... 71 00:05:14,454 --> 00:05:25,569 Floor area is going to be equal to 10.1 feet times 12.07 feet, 72 00:05:25,569 --> 00:05:31,836 so that will give us, let's calculate it. 73 00:05:31,836 --> 00:05:42,406 It is 10.1 times 12.07 feet, it gives a 121.907. 74 00:05:42,406 --> 00:05:46,372 So this equal to - let's scroll over a little bit to the right - 75 00:05:46,372 --> 00:05:49,380 this is equal to - a little bit more over the right - 76 00:05:49,380 --> 00:05:56,549 this is equal to 121.907 feet squared, or squared feet. 77 00:05:56,549 --> 00:05:59,132 Now, we are not done with our calculation, 78 00:05:59,132 --> 00:06:00,714 but there might be a temptation right here, 79 00:06:00,714 --> 00:06:03,308 say look, I have 4 significant figures here, 80 00:06:03,308 --> 00:06:05,628 I have 3 significant figures over here, 81 00:06:05,628 --> 00:06:07,569 there would be a temptation to say, 82 00:06:07,569 --> 00:06:10,833 "Look, my area should not have more then 3 significant figures." 83 00:06:10,833 --> 00:06:14,903 And that temptation would be OK, if this is all you are looking for. 84 00:06:14,903 --> 00:06:18,464 If the final answer you are looking for was the area of the floor. 85 00:06:18,464 --> 00:06:20,842 But we are not done with our calculation, 86 00:06:20,842 --> 00:06:25,381 we want to figure out how many of these tiles will fit into this area. 87 00:06:25,381 --> 00:06:27,214 So the general rule of thumb, 88 00:06:27,214 --> 00:06:29,235 because you don't want to loose information, 89 00:06:29,235 --> 00:06:31,434 the general thumb is: 90 00:06:31,434 --> 00:06:35,378 don't round the significant figures until you are done with the calculation. 91 00:06:35,378 --> 00:06:39,698 Especially if you are just doing a bunch of multiplying and dividing 92 00:06:39,698 --> 00:06:41,842 because otherwise if you round here, 93 00:06:41,842 --> 00:06:45,636 you actually will introduce more error into your calculation than you'd want to. 94 00:06:45,636 --> 00:06:47,988 So what you do is you keep it as kind of a full number. 95 00:06:47,988 --> 00:06:51,287 Now you do the division. So let's do the division. 96 00:06:51,287 --> 00:06:56,253 So the tiles per floor... tiles per floor. 97 00:06:56,253 --> 00:07:00,789 I guess we could say my bathroom or tiles in the bathroom, 98 00:07:00,789 --> 00:07:06,406 tiles fitting in bathroom, on the floor of this bathroom. 99 00:07:06,406 --> 00:07:12,502 It would be the area of the bathroom, so 121.907 feet squared, 100 00:07:12,502 --> 00:07:14,435 divided by the area of the tile, 101 00:07:14,435 --> 00:07:19,002 divided by 1.07 feet squared. 102 00:07:19,002 --> 00:07:21,307 And ones again, let me get the calculator out. 103 00:07:21,307 --> 00:07:29,767 So we have 121.907 divided by 1.07, 104 00:07:29,767 --> 00:07:32,701 and you get this crazy thing with all of these digits, 105 00:07:32,701 --> 00:07:34,497 but this is going to be our final answer, 106 00:07:34,497 --> 00:07:36,899 so here we do care about significant figures. 107 00:07:36,899 --> 00:07:38,835 So tiles fitting in the bathroom, 108 00:07:38,835 --> 00:07:41,010 we get something that is actually just keeps going, 109 00:07:41,010 --> 00:07:43,090 so it's... Let me write this in a new color. 110 00:07:43,090 --> 00:07:52,175 We got 113.931775701 - and actually it just keeps going - feet squared. 111 00:07:52,175 --> 00:07:53,567 And this is the final answer. 112 00:07:53,567 --> 00:07:57,100 We cared about how many tiles will fit onto this bathroom floor, 113 00:07:57,100 --> 00:07:59,508 now the significant figures come into play. 114 00:07:59,508 --> 00:08:01,342 And the way to think about this: 115 00:08:01,342 --> 00:08:06,837 I have 4 significant figures over here, I have 2 significant figures here, 116 00:08:06,837 --> 00:08:09,300 I have 3 significant figures over here, 117 00:08:09,300 --> 00:08:13,166 and since we did just a bunch of multiplying and dividing, in general... 118 00:08:13,166 --> 00:08:17,258 Since we did a bunch of multiplying and dividing we have to have the minimum, 119 00:08:17,258 --> 00:08:20,774 whatever is the minimum significant figures of the things we computed with, 120 00:08:20,774 --> 00:08:23,923 that's how many significant figures we can have in our final answer. 121 00:08:23,923 --> 00:08:28,434 We'll make this clear: this has 2 significant figures, but this is 3: the 1, the 0 and the 1. 122 00:08:28,434 --> 00:08:32,170 So our final answer can only the 3 significant figures. 123 00:08:32,170 --> 00:08:34,034 3 significant figures. 124 00:08:34,034 --> 00:08:40,844 So we need to round to the nearest foot. The next digit over is a 9, so we need to round up. 125 00:08:40,844 --> 00:08:42,422 So we are going to round up. 126 00:08:42,422 --> 00:08:48,767 So this would get us to 114. Actually this units aren't squared feet, this is in tiles. 127 00:08:48,767 --> 00:08:56,432 This is feet divided by feet, and so this is going to be 114, 114 tiles. 128 00:08:56,432 --> 00:08:59,031 Obviously it is not going to be exactly 114 tiles, 129 00:08:59,031 --> 00:09:03,172 but based on the precision of the measurements we have done, 130 00:09:03,172 --> 00:09:05,031 we can say 114 tiles. 131 00:09:05,031 --> 00:09:09,305 Now what I have just showed you right here what we multiply and divide measurements 132 00:09:09,305 --> 00:09:11,367 that has a certain number of significant figures. 133 00:09:11,367 --> 00:09:15,434 The general rule of thumb is whatever the minimum number of significant figures 134 00:09:15,434 --> 00:09:18,502 in any of the numbers calculated, that is how many significant figures... 135 00:09:18,502 --> 00:09:21,505 that is the least number is the number of significant figure 136 00:09:21,505 --> 00:09:23,767 in your final quotient or product or answer. 137 00:09:23,767 --> 00:09:29,921 When you do addition and subtraction, it's a little bit different and we will cover that in the next video.