[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.89,0:00:03.77,Default,,0000,0000,0000,,I'll now show you how\Nto convert a fraction Dialogue: 0,0:00:03.77,0:00:04.92,Default,,0000,0000,0000,,into a decimal. Dialogue: 0,0:00:04.92,0:00:06.99,Default,,0000,0000,0000,,And if we have time, maybe\Nwe'll learn how to do a Dialogue: 0,0:00:06.99,0:00:08.73,Default,,0000,0000,0000,,decimal into a fraction. Dialogue: 0,0:00:08.73,0:00:11.42,Default,,0000,0000,0000,,So let's start with, what\NI would say, is a fairly Dialogue: 0,0:00:11.42,0:00:12.48,Default,,0000,0000,0000,,straightforward example. Dialogue: 0,0:00:12.48,0:00:15.21,Default,,0000,0000,0000,,Let's start with\Nthe fraction 1/2. Dialogue: 0,0:00:15.21,0:00:17.39,Default,,0000,0000,0000,,And I want to convert\Nthat into a decimal. Dialogue: 0,0:00:17.39,0:00:20.17,Default,,0000,0000,0000,,So the method I'm going to\Nshow you will always work. Dialogue: 0,0:00:20.17,0:00:22.85,Default,,0000,0000,0000,,What you do is you take the\Ndenominator and you divide Dialogue: 0,0:00:22.85,0:00:24.53,Default,,0000,0000,0000,,it into the numerator. Dialogue: 0,0:00:24.53,0:00:25.51,Default,,0000,0000,0000,,Let's see how that works. Dialogue: 0,0:00:25.51,0:00:29.11,Default,,0000,0000,0000,,So we take the denominator-- is\N2-- and we're going to divide Dialogue: 0,0:00:29.11,0:00:32.28,Default,,0000,0000,0000,,that into the numerator, 1. Dialogue: 0,0:00:32.28,0:00:34.11,Default,,0000,0000,0000,,And you're probably saying,\Nwell, how do I divide 2 into 1? Dialogue: 0,0:00:34.11,0:00:37.01,Default,,0000,0000,0000,,Well, if you remember from the\Ndividing decimals module, we Dialogue: 0,0:00:37.01,0:00:40.22,Default,,0000,0000,0000,,can just add a decimal point\Nhere and add some trailing 0's. Dialogue: 0,0:00:40.22,0:00:42.88,Default,,0000,0000,0000,,We haven't actually changed the\Nvalue of the number, but we're Dialogue: 0,0:00:42.88,0:00:45.26,Default,,0000,0000,0000,,just getting some\Nprecision here. Dialogue: 0,0:00:45.26,0:00:46.70,Default,,0000,0000,0000,,We put the decimal point here. Dialogue: 0,0:00:50.26,0:00:50.65,Default,,0000,0000,0000,,Does 2 go into 1? Dialogue: 0,0:00:50.65,0:00:51.28,Default,,0000,0000,0000,,No. Dialogue: 0,0:00:51.28,0:00:56.18,Default,,0000,0000,0000,,2 goes into 10, so we go 2\Ngoes into 10 five times. Dialogue: 0,0:00:56.18,0:00:59.06,Default,,0000,0000,0000,,5 times 2 is 10. Dialogue: 0,0:00:59.06,0:01:00.05,Default,,0000,0000,0000,,Remainder of 0. Dialogue: 0,0:01:00.05,0:01:01.15,Default,,0000,0000,0000,,We're done. Dialogue: 0,0:01:01.15,0:01:06.68,Default,,0000,0000,0000,,So 1/2 is equal to 0.5. Dialogue: 0,0:01:10.57,0:01:12.05,Default,,0000,0000,0000,,Let's do a slightly harder one. Dialogue: 0,0:01:12.05,0:01:15.00,Default,,0000,0000,0000,,Let's figure out 1/3. Dialogue: 0,0:01:15.00,0:01:19.19,Default,,0000,0000,0000,,Well, once again, we take the\Ndenominator, 3, and we divide Dialogue: 0,0:01:19.19,0:01:20.74,Default,,0000,0000,0000,,it into the numerator. Dialogue: 0,0:01:20.74,0:01:25.47,Default,,0000,0000,0000,,And I'm just going to add a\Nbunch of trailing 0's here. Dialogue: 0,0:01:25.47,0:01:27.80,Default,,0000,0000,0000,,3 goes into-- well, 3\Ndoesn't go into 1. Dialogue: 0,0:01:27.80,0:01:30.15,Default,,0000,0000,0000,,3 goes into 10 three times. Dialogue: 0,0:01:30.15,0:01:32.45,Default,,0000,0000,0000,,3 times 3 is 9. Dialogue: 0,0:01:32.45,0:01:35.72,Default,,0000,0000,0000,,Let's subtract, get a\N1, bring down the 0. Dialogue: 0,0:01:35.72,0:01:37.70,Default,,0000,0000,0000,,3 goes into 10 three times. Dialogue: 0,0:01:37.70,0:01:39.70,Default,,0000,0000,0000,,Actually, this decimal\Npoint is right here. Dialogue: 0,0:01:39.70,0:01:42.71,Default,,0000,0000,0000,,3 times 3 is 9. Dialogue: 0,0:01:42.71,0:01:43.93,Default,,0000,0000,0000,,Do you see a pattern here? Dialogue: 0,0:01:43.93,0:01:45.07,Default,,0000,0000,0000,,We keep getting the same thing. Dialogue: 0,0:01:45.07,0:01:47.35,Default,,0000,0000,0000,,As you see it's\Nactually 0.3333. Dialogue: 0,0:01:47.35,0:01:48.83,Default,,0000,0000,0000,,It goes on forever. Dialogue: 0,0:01:48.83,0:01:52.16,Default,,0000,0000,0000,,And a way to actually represent\Nthis, obviously you can't write Dialogue: 0,0:01:52.16,0:01:54.02,Default,,0000,0000,0000,,an infinite number of 3's. Dialogue: 0,0:01:54.02,0:02:00.43,Default,,0000,0000,0000,,Is you could just write 0.--\Nwell, you could write 0.33 Dialogue: 0,0:02:00.43,0:02:03.06,Default,,0000,0000,0000,,repeating, which means that\Nthe 0.33 will go on forever. Dialogue: 0,0:02:03.06,0:02:06.96,Default,,0000,0000,0000,,Or you can actually even\Nsay 0.3 repeating. Dialogue: 0,0:02:06.96,0:02:08.63,Default,,0000,0000,0000,,Although I tend to\Nsee this more often. Dialogue: 0,0:02:08.63,0:02:09.84,Default,,0000,0000,0000,,Maybe I'm just mistaken. Dialogue: 0,0:02:09.84,0:02:12.41,Default,,0000,0000,0000,,But in general, this line on\Ntop of the decimal means Dialogue: 0,0:02:12.41,0:02:17.32,Default,,0000,0000,0000,,that this number pattern\Nrepeats indefinitely. Dialogue: 0,0:02:17.32,0:02:25.21,Default,,0000,0000,0000,,So 1/3 is equal to 0.33333\Nand it goes on forever. Dialogue: 0,0:02:25.21,0:02:29.77,Default,,0000,0000,0000,,Another way of writing\Nthat is 0.33 repeating. Dialogue: 0,0:02:29.77,0:02:33.40,Default,,0000,0000,0000,,Let's do a couple of, maybe a\Nlittle bit harder, but they Dialogue: 0,0:02:33.40,0:02:35.06,Default,,0000,0000,0000,,all follow the same pattern. Dialogue: 0,0:02:35.06,0:02:36.89,Default,,0000,0000,0000,,Let me pick some weird numbers. Dialogue: 0,0:02:40.47,0:02:41.89,Default,,0000,0000,0000,,Let me actually do an\Nimproper fraction. Dialogue: 0,0:02:41.89,0:02:49.05,Default,,0000,0000,0000,,Let me say 17/9. Dialogue: 0,0:02:49.05,0:02:50.16,Default,,0000,0000,0000,,So here, it's interesting. Dialogue: 0,0:02:50.16,0:02:52.26,Default,,0000,0000,0000,,The numerator is bigger\Nthan the denominator. Dialogue: 0,0:02:52.26,0:02:54.20,Default,,0000,0000,0000,,So actually we're going to\Nget a number larger than 1. Dialogue: 0,0:02:54.20,0:02:55.27,Default,,0000,0000,0000,,But let's work it out. Dialogue: 0,0:02:55.27,0:03:00.59,Default,,0000,0000,0000,,So we take 9 and we\Ndivide it into 17. Dialogue: 0,0:03:00.59,0:03:06.00,Default,,0000,0000,0000,,And let's add some trailing 0's\Nfor the decimal point here. Dialogue: 0,0:03:06.00,0:03:08.73,Default,,0000,0000,0000,,So 9 goes into 17 one time. Dialogue: 0,0:03:08.73,0:03:11.26,Default,,0000,0000,0000,,1 times 9 is 9. Dialogue: 0,0:03:11.26,0:03:14.04,Default,,0000,0000,0000,,17 minus 9 is 8. Dialogue: 0,0:03:14.04,0:03:16.24,Default,,0000,0000,0000,,Bring down a 0. Dialogue: 0,0:03:16.24,0:03:20.08,Default,,0000,0000,0000,,9 goes into 80-- well, we know\Nthat 9 times 9 is 81, so it has Dialogue: 0,0:03:20.08,0:03:21.83,Default,,0000,0000,0000,,to go into it only eight times\Nbecause it can't go Dialogue: 0,0:03:21.83,0:03:23.23,Default,,0000,0000,0000,,into it nine times. Dialogue: 0,0:03:23.23,0:03:27.01,Default,,0000,0000,0000,,8 times 9 is 72. Dialogue: 0,0:03:27.01,0:03:29.56,Default,,0000,0000,0000,,80 minus 72 is 8. Dialogue: 0,0:03:29.56,0:03:30.77,Default,,0000,0000,0000,,Bring down another 0. Dialogue: 0,0:03:30.77,0:03:32.26,Default,,0000,0000,0000,,I think we see a\Npattern forming again. Dialogue: 0,0:03:32.26,0:03:35.99,Default,,0000,0000,0000,,9 goes into 80 eight times. Dialogue: 0,0:03:35.99,0:03:40.82,Default,,0000,0000,0000,,8 times 9 is 72. Dialogue: 0,0:03:40.82,0:03:44.35,Default,,0000,0000,0000,,And clearly, I could keep\Ndoing this forever and Dialogue: 0,0:03:44.35,0:03:46.79,Default,,0000,0000,0000,,we'd keep getting 8's. Dialogue: 0,0:03:46.79,0:03:53.74,Default,,0000,0000,0000,,So we see 17 divided by 9 is\Nequal to 1.88 where the 0.88 Dialogue: 0,0:03:53.74,0:03:56.08,Default,,0000,0000,0000,,actually repeats forever. Dialogue: 0,0:03:56.08,0:03:59.20,Default,,0000,0000,0000,,Or, if we actually wanted to\Nround this we could say that Dialogue: 0,0:03:59.20,0:04:01.43,Default,,0000,0000,0000,,that is also equal to 1.--\Ndepending where we wanted Dialogue: 0,0:04:01.43,0:04:02.86,Default,,0000,0000,0000,,to round it, what place. Dialogue: 0,0:04:02.86,0:04:05.99,Default,,0000,0000,0000,,We could say roughly 1.89. Dialogue: 0,0:04:05.99,0:04:07.48,Default,,0000,0000,0000,,Or we could round in\Na different place. Dialogue: 0,0:04:07.48,0:04:09.31,Default,,0000,0000,0000,,I rounded in the 100's place. Dialogue: 0,0:04:09.31,0:04:11.35,Default,,0000,0000,0000,,But this is actually\Nthe exact answer. Dialogue: 0,0:04:11.35,0:04:15.13,Default,,0000,0000,0000,,17/9 is equal to 1.88. Dialogue: 0,0:04:15.13,0:04:17.38,Default,,0000,0000,0000,,I actually might do a separate\Nmodule, but how would we write Dialogue: 0,0:04:17.38,0:04:20.73,Default,,0000,0000,0000,,this as a mixed number? Dialogue: 0,0:04:20.73,0:04:23.03,Default,,0000,0000,0000,,Well actually, I'm going\Nto do that in a separate. Dialogue: 0,0:04:23.03,0:04:24.39,Default,,0000,0000,0000,,I don't want to\Nconfuse you for now. Dialogue: 0,0:04:24.39,0:04:25.38,Default,,0000,0000,0000,,Let's do a couple\Nmore problems. Dialogue: 0,0:04:28.56,0:04:29.98,Default,,0000,0000,0000,,Let me do a real weird one. Dialogue: 0,0:04:29.98,0:04:34.36,Default,,0000,0000,0000,,Let me do 17/93. Dialogue: 0,0:04:34.36,0:04:36.71,Default,,0000,0000,0000,,What does that equal\Nas a decimal? Dialogue: 0,0:04:36.71,0:04:39.13,Default,,0000,0000,0000,,Well, we do the same thing. Dialogue: 0,0:04:39.13,0:04:45.63,Default,,0000,0000,0000,,93 goes into-- I make a really\Nlong line up here because Dialogue: 0,0:04:45.63,0:04:47.93,Default,,0000,0000,0000,,I don't know how many\Ndecimal places we'll do. Dialogue: 0,0:04:50.57,0:04:53.22,Default,,0000,0000,0000,,And remember, it's always the\Ndenominator being divided Dialogue: 0,0:04:53.22,0:04:54.93,Default,,0000,0000,0000,,into the numerator. Dialogue: 0,0:04:54.93,0:04:56.95,Default,,0000,0000,0000,,This used to confuse me a lot\Nof times because you're often Dialogue: 0,0:04:56.95,0:04:59.63,Default,,0000,0000,0000,,dividing a larger number\Ninto a smaller number. Dialogue: 0,0:04:59.63,0:05:02.58,Default,,0000,0000,0000,,So 93 goes into 17 zero times. Dialogue: 0,0:05:02.58,0:05:04.08,Default,,0000,0000,0000,,There's a decimal. Dialogue: 0,0:05:04.08,0:05:05.99,Default,,0000,0000,0000,,93 goes into 170? Dialogue: 0,0:05:05.99,0:05:07.27,Default,,0000,0000,0000,,Goes into it one time. Dialogue: 0,0:05:07.27,0:05:11.41,Default,,0000,0000,0000,,1 times 93 is 93. Dialogue: 0,0:05:11.41,0:05:14.37,Default,,0000,0000,0000,,170 minus 93 is 77. Dialogue: 0,0:05:17.98,0:05:20.36,Default,,0000,0000,0000,,Bring down the 0. Dialogue: 0,0:05:20.36,0:05:23.70,Default,,0000,0000,0000,,93 goes into 770? Dialogue: 0,0:05:23.70,0:05:24.66,Default,,0000,0000,0000,,Let's see. Dialogue: 0,0:05:24.66,0:05:29.12,Default,,0000,0000,0000,,It will go into it, I think,\Nroughly eight times. Dialogue: 0,0:05:29.12,0:05:33.33,Default,,0000,0000,0000,,8 times 3 is 24. Dialogue: 0,0:05:33.33,0:05:35.97,Default,,0000,0000,0000,,8 times 9 is 72. Dialogue: 0,0:05:35.97,0:05:39.73,Default,,0000,0000,0000,,Plus 2 is 74. Dialogue: 0,0:05:39.73,0:05:42.19,Default,,0000,0000,0000,,And then we subtract. Dialogue: 0,0:05:42.19,0:05:43.99,Default,,0000,0000,0000,,10 and 6. Dialogue: 0,0:05:43.99,0:05:46.71,Default,,0000,0000,0000,,It's equal to 26. Dialogue: 0,0:05:46.71,0:05:47.76,Default,,0000,0000,0000,,Then we bring down another 0. Dialogue: 0,0:05:47.76,0:05:52.80,Default,,0000,0000,0000,,93 goes into 26--\Nabout two times. Dialogue: 0,0:05:52.80,0:05:57.02,Default,,0000,0000,0000,,2 times 3 is 6. Dialogue: 0,0:05:57.02,0:05:58.70,Default,,0000,0000,0000,,18. Dialogue: 0,0:05:58.70,0:05:59.92,Default,,0000,0000,0000,,This is 74. Dialogue: 0,0:06:03.12,0:06:03.93,Default,,0000,0000,0000,,0. Dialogue: 0,0:06:03.93,0:06:06.38,Default,,0000,0000,0000,,So we could keep going. Dialogue: 0,0:06:06.38,0:06:08.03,Default,,0000,0000,0000,,We could keep figuring\Nout the decimal points. Dialogue: 0,0:06:08.03,0:06:10.02,Default,,0000,0000,0000,,You could do this indefinitely. Dialogue: 0,0:06:10.02,0:06:12.09,Default,,0000,0000,0000,,But if you wanted to at least\Nget an approximation, you would Dialogue: 0,0:06:12.09,0:06:23.49,Default,,0000,0000,0000,,say 17 goes into 93 0.-- or\N17/93 is equal to 0.182 and Dialogue: 0,0:06:23.49,0:06:25.02,Default,,0000,0000,0000,,then the decimals\Nwill keep going. Dialogue: 0,0:06:25.02,0:06:27.17,Default,,0000,0000,0000,,And you can keep doing\Nit if you want. Dialogue: 0,0:06:27.17,0:06:28.65,Default,,0000,0000,0000,,If you actually saw this on\Nexam they'd probably tell Dialogue: 0,0:06:28.65,0:06:29.64,Default,,0000,0000,0000,,you to stop at some point. Dialogue: 0,0:06:29.64,0:06:31.65,Default,,0000,0000,0000,,You know, round it to the\Nnearest hundredths or Dialogue: 0,0:06:31.65,0:06:33.61,Default,,0000,0000,0000,,thousandths place. Dialogue: 0,0:06:33.61,0:06:36.55,Default,,0000,0000,0000,,And just so you know, let's try\Nto convert it the other way, Dialogue: 0,0:06:36.55,0:06:37.83,Default,,0000,0000,0000,,from decimals to fractions. Dialogue: 0,0:06:37.83,0:06:40.09,Default,,0000,0000,0000,,Actually, this is, I\Nthink, you'll find a Dialogue: 0,0:06:40.09,0:06:42.30,Default,,0000,0000,0000,,much easier thing to do. Dialogue: 0,0:06:42.30,0:06:49.81,Default,,0000,0000,0000,,If I were to ask you what\N0.035 is as a fraction? Dialogue: 0,0:06:49.81,0:06:56.84,Default,,0000,0000,0000,,Well, all you do is you say,\Nwell, 0.035, we could write it Dialogue: 0,0:06:56.84,0:07:05.13,Default,,0000,0000,0000,,this way-- we could write\Nthat's the same thing as 03-- Dialogue: 0,0:07:05.13,0:07:06.30,Default,,0000,0000,0000,,well, I shouldn't write 035. Dialogue: 0,0:07:06.30,0:07:10.70,Default,,0000,0000,0000,,That's the same\Nthing as 35/1,000. Dialogue: 0,0:07:10.70,0:07:11.58,Default,,0000,0000,0000,,And you're probably\Nsaying, Sal, how did Dialogue: 0,0:07:11.58,0:07:14.12,Default,,0000,0000,0000,,you know it's 35/1000? Dialogue: 0,0:07:14.12,0:07:18.59,Default,,0000,0000,0000,,Well because we went to 3--\Nthis is the 10's place. Dialogue: 0,0:07:18.59,0:07:20.23,Default,,0000,0000,0000,,Tenths not 10's. Dialogue: 0,0:07:20.23,0:07:21.36,Default,,0000,0000,0000,,This is hundreths. Dialogue: 0,0:07:21.36,0:07:23.23,Default,,0000,0000,0000,,This is the thousandths place. Dialogue: 0,0:07:23.23,0:07:25.89,Default,,0000,0000,0000,,So we went to 3 decimals\Nof significance. Dialogue: 0,0:07:25.89,0:07:29.26,Default,,0000,0000,0000,,So this is 35 thousandths. Dialogue: 0,0:07:29.26,0:07:38.65,Default,,0000,0000,0000,,If the decimal was let's\Nsay, if it was 0.030. Dialogue: 0,0:07:38.65,0:07:40.14,Default,,0000,0000,0000,,There's a couple of ways\Nwe could say this. Dialogue: 0,0:07:40.14,0:07:42.49,Default,,0000,0000,0000,,Well, we could say, oh well\Nwe got to 3-- we went to Dialogue: 0,0:07:42.49,0:07:43.57,Default,,0000,0000,0000,,the thousandths Place. Dialogue: 0,0:07:43.57,0:07:48.24,Default,,0000,0000,0000,,So this is the same\Nthing as 30/1,000. Dialogue: 0,0:07:48.24,0:07:48.61,Default,,0000,0000,0000,,or. Dialogue: 0,0:07:48.61,0:07:55.55,Default,,0000,0000,0000,,We could have also said, well,\N0.030 is the same thing as Dialogue: 0,0:07:55.55,0:08:02.71,Default,,0000,0000,0000,,0.03 because this 0 really\Ndoesn't add any value. Dialogue: 0,0:08:02.71,0:08:05.92,Default,,0000,0000,0000,,If we have 0.03 then we're only\Ngoing to the hundredths place. Dialogue: 0,0:08:05.92,0:08:11.10,Default,,0000,0000,0000,,So this is the same\Nthing as 3/100. Dialogue: 0,0:08:11.10,0:08:13.16,Default,,0000,0000,0000,,So let me ask you, are\Nthese two the same? Dialogue: 0,0:08:16.33,0:08:16.67,Default,,0000,0000,0000,,Well, yeah. Dialogue: 0,0:08:16.67,0:08:17.68,Default,,0000,0000,0000,,Sure they are. Dialogue: 0,0:08:17.68,0:08:20.06,Default,,0000,0000,0000,,If we divide both the numerator\Nand the denominator of both of Dialogue: 0,0:08:20.06,0:08:24.89,Default,,0000,0000,0000,,these expressions by\N10 we get 3/100. Dialogue: 0,0:08:24.89,0:08:26.22,Default,,0000,0000,0000,,Let's go back to this case. Dialogue: 0,0:08:26.22,0:08:27.55,Default,,0000,0000,0000,,Are we done with this? Dialogue: 0,0:08:27.55,0:08:30.12,Default,,0000,0000,0000,,Is 35/1,000-- I\Nmean, it's right. Dialogue: 0,0:08:30.12,0:08:31.66,Default,,0000,0000,0000,,That is a fraction. Dialogue: 0,0:08:31.66,0:08:32.58,Default,,0000,0000,0000,,35/1,000. Dialogue: 0,0:08:32.58,0:08:35.44,Default,,0000,0000,0000,,But if we wanted to simplify it\Neven more looks like we could Dialogue: 0,0:08:35.44,0:08:38.53,Default,,0000,0000,0000,,divide both the numerator\Nand the denominator by 5. Dialogue: 0,0:08:38.53,0:08:40.86,Default,,0000,0000,0000,,And then, just to get\Nit into simplest form, Dialogue: 0,0:08:40.86,0:08:47.28,Default,,0000,0000,0000,,that equals 7/200. Dialogue: 0,0:08:47.28,0:08:51.02,Default,,0000,0000,0000,,And if we wanted to convert\N7/200 into a decimal using the Dialogue: 0,0:08:51.02,0:08:54.15,Default,,0000,0000,0000,,technique we just did, so we\Nwould do 200 goes into Dialogue: 0,0:08:54.15,0:08:56.12,Default,,0000,0000,0000,,7 and figure it out. Dialogue: 0,0:08:56.12,0:09:00.17,Default,,0000,0000,0000,,We should get 0.035. Dialogue: 0,0:09:00.17,0:09:02.65,Default,,0000,0000,0000,,I'll leave that up to\Nyou as an exercise. Dialogue: 0,0:09:02.65,0:09:05.37,Default,,0000,0000,0000,,Hopefully now you get at least\Nan initial understanding of how Dialogue: 0,0:09:05.37,0:09:09.32,Default,,0000,0000,0000,,to convert a fraction into a\Ndecimal and maybe vice versa. Dialogue: 0,0:09:09.32,0:09:11.84,Default,,0000,0000,0000,,And if you don't, just do\Nsome of the practices. Dialogue: 0,0:09:11.84,0:09:16.99,Default,,0000,0000,0000,,And I will also try to record\Nanother module on this Dialogue: 0,0:09:16.99,0:09:18.88,Default,,0000,0000,0000,,or another presentation. Dialogue: 0,0:09:18.88,0:09:20.09,Default,,0000,0000,0000,,Have fun with the exercises.