1 00:00:00,710 --> 00:00:03,830 By two numbers, we're having different type of numbers. 2 00:00:03,860 --> 00:00:09,470 We can present in Biton, we shall be discussing on that number data types. 3 00:00:09,560 --> 00:00:12,440 So pite on support street number data types. 4 00:00:12,620 --> 00:00:14,210 The first one is the indigent. 5 00:00:14,720 --> 00:00:18,720 These indigent numbers like your one hundred two zero three zero. 6 00:00:18,770 --> 00:00:22,100 Something like this as an example, flooding by numbers. 7 00:00:22,380 --> 00:00:27,440 These examples are given and complex numbers are to be written in this particular format. 8 00:00:27,650 --> 00:00:31,430 So like your three plus four G five plus 10 G. 9 00:00:31,550 --> 00:00:40,520 In this way we can use a type function to know which class available are a belongs to an instance function 10 00:00:40,550 --> 00:00:44,210 to check if it is belong to a certain particular class or not. 11 00:00:44,900 --> 00:00:46,250 So we are having two functions. 12 00:00:46,250 --> 00:00:49,160 One is a type which will tell the type of the function. 13 00:00:49,430 --> 00:00:54,530 Another one is the instance which will tell whether this particular a variable is object type or not. 14 00:00:55,790 --> 00:00:59,480 Why integers can be of any lend a floating. 15 00:00:59,510 --> 00:01:01,070 My number is accurate. 16 00:01:01,260 --> 00:01:04,160 Only up to 15 decimal places. 17 00:01:04,430 --> 00:01:08,680 There is a sixth in the decimal place will be incorrect in that case. 18 00:01:09,080 --> 00:01:11,940 So that is a decision we are having for the floating by number. 19 00:01:12,170 --> 00:01:17,050 But in case of individuals while integers, it can be of any length numbers. 20 00:01:17,150 --> 00:01:19,520 We deal with everyday a decimal. 21 00:01:19,550 --> 00:01:22,040 That is the best 10 number system. 22 00:01:22,120 --> 00:01:27,290 Python can also express binary octal and hexadecimal numbers. 23 00:01:27,380 --> 00:01:33,680 Also, as computer programmers, generally embedded programmers need to work with the binary. 24 00:01:34,060 --> 00:01:37,610 The binary number system is having the best two or the hexadecimal. 25 00:01:37,640 --> 00:01:43,010 That is the best sixteen and opto, that is the best eight number systems in Python. 26 00:01:43,010 --> 00:01:49,780 We can present these numbers by appropriately placing a prefix before that number. 27 00:01:49,850 --> 00:01:51,080 Now, what are the prefix? 28 00:01:51,560 --> 00:01:58,920 So here to see we can write here as Gedo Small B or Gedo capital B as a binary number prefix. 29 00:01:59,210 --> 00:02:07,310 We're having this Gedo small or or zero capital law as Opteron number prefix, but having zero small 30 00:02:07,310 --> 00:02:11,780 X or Gedo capital X as hexadecimal number prefix. 31 00:02:11,990 --> 00:02:15,470 So these are the prefix we are having to represent the respective number. 32 00:02:17,160 --> 00:02:20,310 No type conversion from one type to another type. 33 00:02:20,370 --> 00:02:22,000 We can do the conversions accordingly. 34 00:02:22,380 --> 00:02:26,410 We can also use the building functions like your iron deep. 35 00:02:26,850 --> 00:02:34,400 We can convert to their respective digit float and complex functions to convert between types explicitly. 36 00:02:34,650 --> 00:02:41,520 These functions can even convert from strings so it can take a string as input and convert it to integer. 37 00:02:41,820 --> 00:02:43,230 In this case, convert to float. 38 00:02:43,320 --> 00:02:49,110 In this case and convert the conflicts complex number in the using this particular complex function. 39 00:02:49,560 --> 00:02:55,200 So I think let us go for one demonstration where we'll be discussing how these numbers can be operated. 40 00:02:55,380 --> 00:02:56,280 Can be handwrote. 41 00:02:56,490 --> 00:03:03,720 Can be doing the typecasting in about python coding numbers in Bryton can have merely three different 42 00:03:03,720 --> 00:03:04,380 data types. 43 00:03:04,980 --> 00:03:06,270 First one is the integer. 44 00:03:06,690 --> 00:03:07,920 So here you see the value. 45 00:03:07,920 --> 00:03:09,250 One is equal to 100. 46 00:03:09,390 --> 00:03:16,170 So this 100 is of type integer and then we're having the next one as flawed in this offload value. 47 00:03:16,210 --> 00:03:17,900 Two is the goal 224. 48 00:03:18,000 --> 00:03:20,060 So it is of the type float class. 49 00:03:20,610 --> 00:03:25,780 And this particular float will always have some decimal point here and fractional part will be there. 50 00:03:26,490 --> 00:03:30,120 And then you are having the another type that is known as a come on plex. 51 00:03:30,300 --> 00:03:36,450 And this complex type numbers will be expressed in the form of the scripting plus six J. 52 00:03:36,780 --> 00:03:38,640 So it is one of the examples we have given. 53 00:03:39,240 --> 00:03:41,810 So we are having three different types added. 54 00:03:42,240 --> 00:03:43,140 One is the iron. 55 00:03:43,280 --> 00:03:44,590 The next one is a float. 56 00:03:44,730 --> 00:03:46,460 And the last one is a complex class. 57 00:03:46,560 --> 00:03:53,640 In about Biton, an integer and floating by numbers are separated by the presence of our absence of 58 00:03:53,640 --> 00:03:54,570 that decimal point. 59 00:03:54,990 --> 00:03:58,080 So in case a five foot eight, only five, it is an integer. 60 00:03:58,110 --> 00:04:01,550 But if we write the five Bunjil rule, it will be up that I float. 61 00:04:02,410 --> 00:04:07,500 Okay, so now here you see where having this value one initialize with the value one hundred and then 62 00:04:07,540 --> 00:04:09,690 we are going for print type of value. 63 00:04:10,410 --> 00:04:16,680 And also we are checking is instance value on I in deep value unflawed and value one complex. 64 00:04:17,100 --> 00:04:23,480 If I execute this particular part we are getting this type as class type I N.T. and this is in stand's 65 00:04:23,480 --> 00:04:25,200 will always return a boolean. 66 00:04:25,430 --> 00:04:28,740 It will check that this value one is of the type I enter or not. 67 00:04:29,260 --> 00:04:30,210 And that is true here. 68 00:04:30,270 --> 00:04:33,690 But in case of load and complex, it is returning false. 69 00:04:34,170 --> 00:04:37,610 Similarly, you're are doing the same type of testing here in case of error too. 70 00:04:38,040 --> 00:04:44,760 If I go on executing, we're getting the record output so value to comma I.A. if we pass these two parameters 71 00:04:44,760 --> 00:04:47,370 to ease instance, I'm getting the output falls. 72 00:04:47,640 --> 00:04:53,460 But here in this case, as this value is Opdyke flawed, so is instanced value to offload will return 73 00:04:53,460 --> 00:04:56,850 true and value to comma complex return false. 74 00:04:57,600 --> 00:04:59,640 So now let us go for this complex. 75 00:05:00,780 --> 00:05:04,600 So here we are having value three Ziegel, two feet deep plus six J. 76 00:05:05,100 --> 00:05:08,100 So if we go on executing, we're getting the output like this. 77 00:05:08,110 --> 00:05:09,300 So in gets up. 78 00:05:09,330 --> 00:05:13,850 I ntn because of flawed with there is instance method we are getting this false. 79 00:05:14,130 --> 00:05:17,550 But with the complex is instance Vello 3Com a complex. 80 00:05:17,640 --> 00:05:19,050 It is returning true here. 81 00:05:19,560 --> 00:05:25,500 So in this way we have tested that how that number in stands can be tested or the number type can be 82 00:05:25,500 --> 00:05:27,000 tested using the method. 83 00:05:27,360 --> 00:05:31,300 Is instance this Biton in Jessup up Iten. 84 00:05:31,350 --> 00:05:37,320 Also we can have other different corresponding representations of data. 85 00:05:37,590 --> 00:05:44,070 There is a binary which will have the best two higson hexadecimal which will be having the best 16 and 86 00:05:44,100 --> 00:05:46,380 octal which will be having the best eight here. 87 00:05:46,860 --> 00:05:51,000 So number we deal with about every day are having the best 10. 88 00:05:51,240 --> 00:05:52,680 That is about decimal numbers. 89 00:05:52,890 --> 00:05:55,980 But other than this decimal, you can work with the best two. 90 00:05:56,040 --> 00:05:57,480 That is a binary number system. 91 00:05:57,480 --> 00:06:02,030 We are having this hexadecimal with the best 16 and octal with the best eight here. 92 00:06:02,490 --> 00:06:08,160 So to represent one binary number, we can easily write a zero B as a prefix to this number. 93 00:06:08,610 --> 00:06:10,650 You can write this being the capital letter also. 94 00:06:10,920 --> 00:06:16,440 So if we go on printing this G to be one one, G to one, that means this one one G to one is not in 95 00:06:16,440 --> 00:06:24,030 decimal but in binary G2 X and stand for the hexadecimal and G2 all will be standing for this octal 96 00:06:24,030 --> 00:06:24,240 here. 97 00:06:24,660 --> 00:06:27,000 So now let me let me go for the execution. 98 00:06:27,090 --> 00:06:32,520 You can find that if I execute this part I'm getting 13 because eight plus fold. 99 00:06:32,610 --> 00:06:38,110 That is plus one that is Hardan here because this particular places have in the place where you put 100 00:06:38,170 --> 00:06:38,700 up zero. 101 00:06:38,790 --> 00:06:41,600 That is one this particular place places having the place. 102 00:06:41,660 --> 00:06:46,250 But what I want that is to deliver up to that is four and three. 103 00:06:46,530 --> 00:06:47,400 That is eight. 104 00:06:47,700 --> 00:06:48,780 So eight plus four. 105 00:06:48,780 --> 00:06:49,480 Plus one. 106 00:06:49,550 --> 00:06:50,010 Thirteen. 107 00:06:50,310 --> 00:06:51,000 We are getting hit. 108 00:06:51,420 --> 00:06:56,760 So in case of this G2 X, a, b so A's having the value in hexadecimal at ten. 109 00:06:57,150 --> 00:07:00,300 So 16 to the part of one in 10. 110 00:07:00,780 --> 00:07:03,000 We're getting here 160 and B's. 111 00:07:03,030 --> 00:07:03,600 I mean the value. 112 00:07:03,690 --> 00:07:04,140 Eleven. 113 00:07:04,410 --> 00:07:06,630 So eleven into six into the port of zero. 114 00:07:06,840 --> 00:07:08,640 So you are landing with eleven only. 115 00:07:08,970 --> 00:07:10,510 So 160 plus eleven. 116 00:07:10,590 --> 00:07:12,900 We're getting the value one seventy one. 117 00:07:13,560 --> 00:07:16,330 In the last case you can find that it is two into. 118 00:07:16,530 --> 00:07:20,700 It did go to one because it is represented in the terms of octal. 119 00:07:21,030 --> 00:07:24,270 So two into a two to one plus three and two ated Brazil. 120 00:07:24,600 --> 00:07:25,740 So we are getting these values. 121 00:07:25,740 --> 00:07:26,880 Sixteen plus three. 122 00:07:27,150 --> 00:07:28,350 And that is nineteen here. 123 00:07:28,740 --> 00:07:32,760 So in place of writing this small B can also go for the capital B. 124 00:07:33,960 --> 00:07:38,700 This is I'm replacing this one as Capital X and replacing this one as capital. 125 00:07:39,240 --> 00:07:41,910 Then also we are going to get the same output here. 126 00:07:42,240 --> 00:07:48,480 Now, here you see here, we're having this particular value, 10 in terms of integer and thirteen point 127 00:07:48,480 --> 00:07:50,910 four is nothing but a floor data. 128 00:07:51,180 --> 00:07:53,580 So what will happen if you go on printing this one? 129 00:07:53,910 --> 00:07:58,050 So you see the result is being converted to the respective float here. 130 00:07:58,440 --> 00:08:04,950 So operations like addition, subtraction, which all which you deal, which is dealing with this integer 131 00:08:04,980 --> 00:08:10,260 and the float, and then automatically it will be converted to the float implicitly. 132 00:08:11,790 --> 00:08:15,620 So here to see we're having this in digit operand here, we're having this float apparent. 133 00:08:15,930 --> 00:08:21,590 If anyone of our part in this float, then the result will be implicitly converted to the floor type. 134 00:08:22,710 --> 00:08:25,080 So now we are going to have this type conversion. 135 00:08:25,470 --> 00:08:27,990 So ten point five is up that a float. 136 00:08:28,470 --> 00:08:32,280 And if you want to convert it to integer, we can get output like this. 137 00:08:32,400 --> 00:08:35,340 So 10 is getting output is producing output. 138 00:08:35,550 --> 00:08:39,210 So now here we are having this minus twenty point nine nine. 139 00:08:39,240 --> 00:08:41,070 So it is a float type. 140 00:08:41,070 --> 00:08:45,330 So if we do the type custom integer, we're getting this one as minus 20. 141 00:08:45,630 --> 00:08:51,390 So we can find this one that when we are doing the conversion to integer, it is not changing the sign 142 00:08:51,510 --> 00:08:52,550 of the number. 143 00:08:52,950 --> 00:08:54,590 So here we are having this float then. 144 00:08:54,900 --> 00:08:59,850 So this 10 is of the type integer because there is no fractional part, there is no decimal point. 145 00:09:00,150 --> 00:09:02,680 But as I did the type conversion here. 146 00:09:02,820 --> 00:09:04,950 So output has become ten point zero. 147 00:09:05,490 --> 00:09:07,110 Now consider this example. 148 00:09:07,590 --> 00:09:10,810 Data one is equal to two point one plus jitterbugging two. 149 00:09:11,300 --> 00:09:13,800 And you were just printing the value of data one. 150 00:09:14,310 --> 00:09:19,680 So if I exude this code, we're finding that we are expecting we were expecting the value should be 151 00:09:19,680 --> 00:09:24,060 printed as zero point three because zero point one plus two point two should be due to open three. 152 00:09:24,690 --> 00:09:30,070 But you are finding that, but having so many different zeros after that and then 140 is coming. 153 00:09:30,270 --> 00:09:36,210 So it is an error is getting cost due to the hardware of our system, not due to the python. 154 00:09:36,960 --> 00:09:43,770 So if we want to check whether you look plus one plus D2 plus how do you define one plus Japan two is 155 00:09:44,010 --> 00:09:45,090 do you happen three or not. 156 00:09:45,390 --> 00:09:49,830 Then in that case we'll be finding that the condition is giving the output as false. 157 00:09:50,220 --> 00:09:55,290 To overcome this issue, we can use that decimal model that comes with Biton. 158 00:09:55,740 --> 00:10:02,730 And while floating print numbers have the position of 215 decimal places and the decimal model has user 159 00:10:02,730 --> 00:10:04,920 citable position accordingly. 160 00:10:05,460 --> 00:10:07,230 So here you see we're having this data. 161 00:10:07,230 --> 00:10:11,160 One is the call digit lupine one plus zero point to print data one. 162 00:10:11,550 --> 00:10:17,220 So we are getting this output as you do Pinetree and makeable number of zeros and four and then heroes 163 00:10:17,220 --> 00:10:22,860 who we are just doing one calculation that is zero point one point two zero into two point 2.5 zero. 164 00:10:23,100 --> 00:10:24,660 And you are printing the value of data one. 165 00:10:24,690 --> 00:10:26,400 We are getting this trip and you too, as well. 166 00:10:26,940 --> 00:10:30,420 So now from decimal import decimal as a D. 167 00:10:31,020 --> 00:10:35,580 So if you know, do the calculation in this way, you can see the rate in this particular code. 168 00:10:35,670 --> 00:10:38,130 And we are going to print the respective result. 169 00:10:38,470 --> 00:10:42,430 We're getting the value as zero point three, which which was expected. 170 00:10:42,660 --> 00:10:46,530 And for this outcome, we are getting this output as and three point G digital. 171 00:10:46,920 --> 00:10:52,830 So in this way, the problem which we're are facing in case up by tonn can be overcome. 172 00:10:53,190 --> 00:10:59,500 Using the from decimal import decimal here does this dismal day will be in the sparkies. 173 00:11:00,750 --> 00:11:01,620 So here we are. 174 00:11:01,800 --> 00:11:04,210 Use one alias that is as Dehnart. 175 00:11:04,800 --> 00:11:06,570 Now we shall discuss fractions. 176 00:11:06,960 --> 00:11:13,050 Biton provides operations involving fractional numbers through its fractions model. 177 00:11:13,650 --> 00:11:21,170 And this fraction model will help us to convert one fluting by number to a new monitor Doumitt form 178 00:11:21,380 --> 00:11:25,170 where both the new monitor and the denominator will be Opta type integer. 179 00:11:25,770 --> 00:11:28,580 Actually, Fraction has a new monitor and a dual monitor. 180 00:11:28,950 --> 00:11:30,960 And both of which are integers. 181 00:11:31,230 --> 00:11:35,400 And this model has supples for rational number arithmetic. 182 00:11:35,760 --> 00:11:37,590 So let us go for this example here. 183 00:11:38,010 --> 00:11:42,400 So you see that from fractions import fraction as F.. 184 00:11:42,840 --> 00:11:45,060 And this is a respected model at executing here. 185 00:11:45,510 --> 00:11:50,670 So you can find that one point five can be expressed in terms of three by two. 186 00:11:51,090 --> 00:11:57,330 And this three is nothing but one integer new monitor and two is nothing but an integer, which is being 187 00:11:57,390 --> 00:11:59,250 which has been placed as a denominator. 188 00:11:59,790 --> 00:12:01,270 So print F five. 189 00:12:01,320 --> 00:12:02,500 Which will give you the five. 190 00:12:02,880 --> 00:12:04,080 And print F one. 191 00:12:04,080 --> 00:12:04,430 Come off. 192 00:12:04,440 --> 00:12:05,640 I will give you the value. 193 00:12:05,880 --> 00:12:07,290 That is one by five. 194 00:12:07,770 --> 00:12:12,600 So while creating fraction from float, we might get some unusual results. 195 00:12:12,630 --> 00:12:16,730 And it is due to the imperfect binary floating by numberi presentation. 196 00:12:17,290 --> 00:12:21,780 Unfortunately, fraction allows us to instead shift with the string as well. 197 00:12:22,260 --> 00:12:26,520 And this is preferred option when using the decimal numbers. 198 00:12:26,940 --> 00:12:29,410 Now we shall discuss that math model. 199 00:12:29,820 --> 00:12:36,480 Python offers model like math and the random to carry out different mathematics like your trigonometry, 200 00:12:36,780 --> 00:12:40,350 logarithms, probability statistics and etc.. 201 00:12:40,800 --> 00:12:42,790 So just consider this setup code. 202 00:12:43,230 --> 00:12:45,300 So Biton math model. 203 00:12:45,350 --> 00:12:50,940 So we have imported the math and then we have we used multiple different functions available in the 204 00:12:50,940 --> 00:12:51,480 math here. 205 00:12:51,750 --> 00:12:58,020 So by calls log log up, then you XP factorial and signage. 206 00:12:58,290 --> 00:13:00,600 So here is the respective outputs we're getting here. 207 00:13:01,140 --> 00:13:10,010 So if we want to print, if we want to print the absolute opposite, minus twelve point two for if during 208 00:13:10,080 --> 00:13:10,560 this one. 209 00:13:10,810 --> 00:13:17,500 Then in that case, we need not to use that math model here so we can use likely as a B.S. minus. 210 00:13:17,550 --> 00:13:23,320 Well, 24, you can find that we are considered only the magnitude part and assigned part has been ignored. 211 00:13:23,770 --> 00:13:24,880 Now, let us come to this. 212 00:13:25,090 --> 00:13:26,350 That is a random here. 213 00:13:26,770 --> 00:13:32,730 So here to see we are going for the random, random random range that is Hypercom fifteen. 214 00:13:33,070 --> 00:13:34,930 So the initial value is a start value. 215 00:13:34,990 --> 00:13:35,890 Which is optional. 216 00:13:35,950 --> 00:13:40,150 If you don't provide an initial value, the value will become considered as zero. 217 00:13:40,540 --> 00:13:42,420 And the last one, the next one value. 218 00:13:42,460 --> 00:13:47,090 That is a second argument where passing is a mandatory that is the dominating value of the stock below. 219 00:13:47,350 --> 00:13:48,490 And that is exclusive. 220 00:13:48,790 --> 00:13:54,460 Naquin ZF The random numbers will be generated inclusive five to 15 exclusive. 221 00:13:54,790 --> 00:13:59,930 So in this way you can go on printing and we can generate multiple random numbers idea. 222 00:14:00,460 --> 00:14:02,050 So the first value is optional. 223 00:14:02,170 --> 00:14:02,640 That is the. 224 00:14:02,770 --> 00:14:03,850 And there is a start value. 225 00:14:04,120 --> 00:14:05,890 The second value is mandatory. 226 00:14:05,920 --> 00:14:06,830 That is a stop halloo. 227 00:14:07,060 --> 00:14:10,860 Then you can also put another argument, comma after putting comedy at. 228 00:14:11,200 --> 00:14:12,760 That is a that is a step below. 229 00:14:13,270 --> 00:14:18,430 So here we have printed ran drench in between five to 15, four times. 230 00:14:18,460 --> 00:14:19,540 So now you're having this. 231 00:14:19,590 --> 00:14:22,590 Eleven, eight, 14 and 13. 232 00:14:22,630 --> 00:14:26,170 If a executer called once again, we're getting that different set of values. 233 00:14:26,380 --> 00:14:29,230 If we execute a code one second, we're getting different set of values. 234 00:14:29,680 --> 00:14:33,880 So now we are having one loose here, then random dot choice day. 235 00:14:34,090 --> 00:14:39,270 So day is nothing but a list here to see it has picked up the random choices to you. 236 00:14:39,580 --> 00:14:44,310 If you go for execution once again, we're getting this value as do here once again. 237 00:14:44,590 --> 00:14:45,730 So if you go for it again. 238 00:14:47,040 --> 00:14:48,990 You can find that they're getting hit, Mondher. 239 00:14:49,530 --> 00:14:51,120 So now that is a print day. 240 00:14:51,390 --> 00:14:57,810 Now we are going for random NAFLD day and then if we print data, we can find that this is their respective 241 00:14:58,030 --> 00:15:00,150 different ad enjoyment of this list. 242 00:15:00,210 --> 00:15:02,240 Elements, at least elements have suffered. 243 00:15:02,760 --> 00:15:07,950 And then we are having this print random elements in front of Brinda random element that the method 244 00:15:07,950 --> 00:15:08,610 is random. 245 00:15:08,880 --> 00:15:11,520 So we can bring the respective random element here. 246 00:15:11,940 --> 00:15:18,070 So in this way, in this particular program, we have discussed multiple different aspects of offer 247 00:15:18,090 --> 00:15:20,260 number type in about Python. 248 00:15:20,700 --> 00:15:22,280 So let us go for a quick revision. 249 00:15:22,650 --> 00:15:24,390 So type is actually returning. 250 00:15:24,620 --> 00:15:30,480 That type of the variable is instances actually checking whether this particular variable is having 251 00:15:30,480 --> 00:15:31,410 this type or not. 252 00:15:31,650 --> 00:15:35,110 So that's why this is instance is actually turning to outfalls. 253 00:15:35,730 --> 00:15:37,770 So we have tested that one on integer. 254 00:15:37,800 --> 00:15:42,090 We have tested that one on flawed Web district, one on complex numbers. 255 00:15:42,540 --> 00:15:46,350 So here we have we are expressing numbers in terms of binary. 256 00:15:46,500 --> 00:15:51,510 So the prefix will be Gedo B, B can be small liquor or capital letters for the hexadecimal. 257 00:15:51,510 --> 00:15:55,010 The prefix should be Gedo X, X can be Lorqess or in the upper case. 258 00:15:55,270 --> 00:16:00,660 And for the octal we are having this Balou which which will be having the prefixes, Gedo or or can 259 00:16:00,660 --> 00:16:02,280 be in the laughers or apartness. 260 00:16:02,730 --> 00:16:08,280 So here you can find that whenever we are doing some calculations involving integers and float, the 261 00:16:08,280 --> 00:16:11,010 result will get implicitly converted to the float. 262 00:16:11,550 --> 00:16:17,160 But having to describe conversion from this float to the integer from this group to the integer from 263 00:16:17,160 --> 00:16:19,570 this in digital, the float respective outputs idea. 264 00:16:20,250 --> 00:16:21,820 We have discussed this decimal here. 265 00:16:22,110 --> 00:16:23,470 How we can deal with that. 266 00:16:23,490 --> 00:16:25,620 We can have the control over the positions. 267 00:16:26,040 --> 00:16:28,620 And then we're having this byte on fractions. 268 00:16:28,650 --> 00:16:30,630 You can see that how the factions are working. 269 00:16:30,960 --> 00:16:34,560 And then the Met model and also the random model here. 270 00:16:35,010 --> 00:16:39,940 I think now you're getting this idea that how this numbers are getting handled in about by programming. 271 00:16:40,530 --> 00:16:41,670 Thanks for watching this video.