[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.55,0:00:03.61,Default,,0000,0000,0000,,PROBLEM: "Express the rational number 19/27
Dialogue: 0,0:00:03.61,0:00:06.54,Default,,0000,0000,0000,,(or 19 27ths) as a terminating decimal
Dialogue: 0,0:00:06.54,0:00:08.67,Default,,0000,0000,0000,,or a decimal that eventually repeats.
Dialogue: 0,0:00:08.67,0:00:10.37,Default,,0000,0000,0000,,Include only the first six digits
Dialogue: 0,0:00:10.37,0:00:12.65,Default,,0000,0000,0000,,of the decimal in your answer."
Dialogue: 0,0:00:12.65,0:00:14.60,Default,,0000,0000,0000,,Let me give this a shot.
Dialogue: 0,0:00:14.60,0:00:18.79,Default,,0000,0000,0000,,So we want to express 19/27 –
Dialogue: 0,0:00:18.79,0:00:23.65,Default,,0000,0000,0000,,which is the same thing as 19 ÷ 27 – as a decimal.
Dialogue: 0,0:00:23.65,0:00:26.35,Default,,0000,0000,0000,,So let's divide 27 into 19.
Dialogue: 0,0:00:26.35,0:00:29.48,Default,,0000,0000,0000,,So 27 going into 19.
Dialogue: 0,0:00:29.48,0:00:31.26,Default,,0000,0000,0000,,And we know it's going to involve some decimals
Dialogue: 0,0:00:31.26,0:00:33.71,Default,,0000,0000,0000,,over here, because 27 is larger than 19,
Dialogue: 0,0:00:33.71,0:00:36.29,Default,,0000,0000,0000,,and it doesn't divide perfectly.
Dialogue: 0,0:00:36.29,0:00:38.13,Default,,0000,0000,0000,,So let's get into this.
Dialogue: 0,0:00:38.13,0:00:39.30,Default,,0000,0000,0000,,So 27 doesn't go into 1.
Dialogue: 0,0:00:39.30,0:00:40.92,Default,,0000,0000,0000,,It doesn't go into 19.
Dialogue: 0,0:00:40.92,0:00:43.99,Default,,0000,0000,0000,,It does go into 190.
Dialogue: 0,0:00:43.99,0:00:47.22,Default,,0000,0000,0000,,And it looks like 27 is roughly 30.
Dialogue: 0,0:00:47.22,0:00:48.79,Default,,0000,0000,0000,,It's a little less than 30.
Dialogue: 0,0:00:48.79,0:00:50.43,Default,,0000,0000,0000,,30 times 6 would be 180.
Dialogue: 0,0:00:50.43,0:00:53.13,Default,,0000,0000,0000,,So let's go with it going 6 times.
Dialogue: 0,0:00:53.13,0:00:54.04,Default,,0000,0000,0000,,Let's see if that works out.
Dialogue: 0,0:00:54.04,0:00:57.40,Default,,0000,0000,0000,,Well, 6 × 7 is 42.
Dialogue: 0,0:00:57.40,0:01:01.60,Default,,0000,0000,0000,,6 × 2 is 12, + 4 is 16.
Dialogue: 0,0:01:01.60,0:01:06.36,Default,,0000,0000,0000,,And when we subtract, 190 - 162 is going to get us –
Dialogue: 0,0:01:06.36,0:01:08.94,Default,,0000,0000,0000,,Actually, we could've had another 27 in there.
Dialogue: 0,0:01:08.94,0:01:10.72,Default,,0000,0000,0000,,Because when we subtract –
Dialogue: 0,0:01:10.72,0:01:12.51,Default,,0000,0000,0000,,So we get a 10 from the 10's place.
Dialogue: 0,0:01:12.51,0:01:13.97,Default,,0000,0000,0000,,So that becomes 8 10's.
Dialogue: 0,0:01:13.97,0:01:15.75,Default,,0000,0000,0000,,This became 28.
Dialogue: 0,0:01:15.75,0:01:17.52,Default,,0000,0000,0000,,So we could have put one more 27 in there.
Dialogue: 0,0:01:17.52,0:01:19.14,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:01:19.14,0:01:22.48,Default,,0000,0000,0000,,So let's put one more 27 in there.
Dialogue: 0,0:01:22.48,0:01:24.33,Default,,0000,0000,0000,,So 7 27's.
Dialogue: 0,0:01:24.33,0:01:26.92,Default,,0000,0000,0000,,7 × 7 is 49.
Dialogue: 0,0:01:26.92,0:01:31.19,Default,,0000,0000,0000,,7 × 2 is 14, + 4 is 18.
Dialogue: 0,0:01:31.19,0:01:33.46,Default,,0000,0000,0000,,And now our remainder is 1.
Dialogue: 0,0:01:33.46,0:01:37.86,Default,,0000,0000,0000,,We can bring down another 0.
Dialogue: 0,0:01:37.86,0:01:39.91,Default,,0000,0000,0000,,27 goes into 10 0 times.
Dialogue: 0,0:01:39.91,0:01:42.15,Default,,0000,0000,0000,,0 × 27 is 0. [Not "10," as Sal states by mistake.]
Dialogue: 0,0:01:42.15,0:01:44.10,Default,,0000,0000,0000,,Subtract – we have a remainder of 10.
Dialogue: 0,0:01:44.10,0:01:46.69,Default,,0000,0000,0000,,But now, we have to bring down another 0.
Dialogue: 0,0:01:46.69,0:01:51.01,Default,,0000,0000,0000,,So let's bring down this 0 right over here.
Dialogue: 0,0:01:51.01,0:01:56.49,Default,,0000,0000,0000,,So now, 27 goes into 100 3 times.
Dialogue: 0,0:01:56.49,0:02:05.94,Default,,0000,0000,0000,,3 × 27 is 60 + 21, is 81.
Dialogue: 0,0:02:05.94,0:02:09.15,Default,,0000,0000,0000,,And then we subtract: 100 - 81.
Dialogue: 0,0:02:09.15,0:02:10.44,Default,,0000,0000,0000,,Well, we could take 100 from
Dialogue: 0,0:02:10.44,0:02:13.33,Default,,0000,0000,0000,,the 100's place, and make it 10 10's.
Dialogue: 0,0:02:13.33,0:02:15.39,Default,,0000,0000,0000,,And then we could take 1 of those 10's from
Dialogue: 0,0:02:15.39,0:02:18.14,Default,,0000,0000,0000,,the 10's place and turn it into 10 1's.
Dialogue: 0,0:02:18.14,0:02:22.39,Default,,0000,0000,0000,,And so 9 10's minus 8 10's is equal to 1 10.
Dialogue: 0,0:02:22.39,0:02:24.72,Default,,0000,0000,0000,,And then 10 -1 is 9.
Dialogue: 0,0:02:24.72,0:02:25.62,Default,,0000,0000,0000,,So it's equal to 19.
Dialogue: 0,0:02:25.62,0:02:26.29,Default,,0000,0000,0000,,You probably –
Dialogue: 0,0:02:26.29,0:02:28.34,Default,,0000,0000,0000,,You might have been able to do that in your head.
Dialogue: 0,0:02:28.34,0:02:29.25,Default,,0000,0000,0000,,And then we have –
Dialogue: 0,0:02:29.25,0:02:30.73,Default,,0000,0000,0000,,And I see something interesting here –
Dialogue: 0,0:02:30.73,0:02:33.59,Default,,0000,0000,0000,,because when we bring down our next 0,
Dialogue: 0,0:02:33.59,0:02:34.90,Default,,0000,0000,0000,,we see 190 again.
Dialogue: 0,0:02:34.90,0:02:36.81,Default,,0000,0000,0000,,We saw 190 up here.
Dialogue: 0,0:02:36.81,0:02:38.33,Default,,0000,0000,0000,,But let's just keep going.
Dialogue: 0,0:02:38.33,0:02:40.57,Default,,0000,0000,0000,,So 27 goes into 190 –
Dialogue: 0,0:02:40.57,0:02:42.65,Default,,0000,0000,0000,,And we already played this game.
Dialogue: 0,0:02:42.65,0:02:44.55,Default,,0000,0000,0000,,It goes into it 7 times.
Dialogue: 0,0:02:44.55,0:02:48.28,Default,,0000,0000,0000,,7 × 27 – we already figured out – was 189.
Dialogue: 0,0:02:48.28,0:02:49.15,Default,,0000,0000,0000,,We subtracted.
Dialogue: 0,0:02:49.15,0:02:50.59,Default,,0000,0000,0000,,We had a remainder of 1.
Dialogue: 0,0:02:50.59,0:02:54.01,Default,,0000,0000,0000,,Then we brought down another 0.
Dialogue: 0,0:02:54.01,0:02:57.31,Default,,0000,0000,0000,,We said 27 goes into 10 0 times.
Dialogue: 0,0:02:57.31,0:02:59.07,Default,,0000,0000,0000,,0 × 27 is 0.
Dialogue: 0,0:02:59.07,0:03:00.26,Default,,0000,0000,0000,,Subtract.
Dialogue: 0,0:03:00.26,0:03:01.64,Default,,0000,0000,0000,,Then you have –
Dialogue: 0,0:03:01.64,0:03:02.94,Default,,0000,0000,0000,,We still have the 10,
Dialogue: 0,0:03:02.94,0:03:07.30,Default,,0000,0000,0000,,but we've got to bring down another 0.
Dialogue: 0,0:03:07.30,0:03:09.08,Default,,0000,0000,0000,,So you have 27, which goes into 100 –
Dialogue: 0,0:03:09.08,0:03:10.44,Default,,0000,0000,0000,,(We've already done this.)
Dialogue: 0,0:03:10.44,0:03:11.60,Default,,0000,0000,0000,,–3 times.
Dialogue: 0,0:03:11.60,0:03:13.75,Default,,0000,0000,0000,,So you see something happening here.
Dialogue: 0,0:03:13.75,0:03:16.67,Default,,0000,0000,0000,,It's 0.703703.
Dialogue: 0,0:03:16.67,0:03:18.95,Default,,0000,0000,0000,,And we're just going to keep repeating 703.
Dialogue: 0,0:03:18.95,0:03:27.22,Default,,0000,0000,0000,,This is going to be equal to 0.703703703703 –
Dialogue: 0,0:03:27.22,0:03:29.72,Default,,0000,0000,0000,,on and on and on forever.
Dialogue: 0,0:03:29.72,0:03:32.27,Default,,0000,0000,0000,,So the notation for representing
Dialogue: 0,0:03:32.27,0:03:34.42,Default,,0000,0000,0000,,a repeating decimal like this
Dialogue: 0,0:03:34.42,0:03:36.40,Default,,0000,0000,0000,,is to write the numbers that repeat –
Dialogue: 0,0:03:36.40,0:03:38.55,Default,,0000,0000,0000,,in this case 7, 0, and 3 –
Dialogue: 0,0:03:38.55,0:03:40.06,Default,,0000,0000,0000,,and then you put a line over all of
Dialogue: 0,0:03:40.06,0:03:40.100,Default,,0000,0000,0000,,the repeating decimal numbers
Dialogue: 0,0:03:40.100,0:03:41.79,Default,,0000,0000,0000,,to indicate that they repeat.
Dialogue: 0,0:03:41.79,0:03:44.98,Default,,0000,0000,0000,,So you put a line over the 7, the 0, and the 3,
Dialogue: 0,0:03:44.98,0:03:47.13,Default,,0000,0000,0000,,which means that the 703 will keep
Dialogue: 0,0:03:47.13,0:03:49.42,Default,,0000,0000,0000,,repeating on and on and on.
Dialogue: 0,0:03:49.42,0:03:52.87,Default,,0000,0000,0000,,So let's actually input it into the answer box now.
Dialogue: 0,0:03:52.87,0:04:02.11,Default,,0000,0000,0000,,So it's 0.703703.
Dialogue: 0,0:04:02.11,0:04:03.34,Default,,0000,0000,0000,,And they tell us to include only
Dialogue: 0,0:04:03.34,0:04:05.84,Default,,0000,0000,0000,,the first six digits of the decimal in your answer.
Dialogue: 0,0:04:05.84,0:04:07.64,Default,,0000,0000,0000,,And they don't tell us to round or approximate –
Dialogue: 0,0:04:07.64,0:04:10.20,Default,,0000,0000,0000,,because, obviously, if they said to round
Dialogue: 0,0:04:10.20,0:04:13.96,Default,,0000,0000,0000,,that final sixth decimal place,
Dialogue: 0,0:04:13.96,0:04:15.02,Default,,0000,0000,0000,,then you would round it up from 6 to 7,
Dialogue: 0,0:04:15.02,0:04:16.11,Default,,0000,0000,0000,,because the next digit is a 7.
Dialogue: 0,0:04:16.11,0:04:17.48,Default,,0000,0000,0000,,But they don't ask us to round.
Dialogue: 0,0:04:17.48,0:04:19.34,Default,,0000,0000,0000,,They just say, "Include only the first six digits
Dialogue: 0,0:04:19.34,0:04:20.99,Default,,0000,0000,0000,,of the decimal in your answer."
Dialogue: 0,0:04:20.99,0:04:23.14,Default,,0000,0000,0000,,So that should do the trick.
Dialogue: 0,0:04:23.14,0:04:24.60,Default,,0000,0000,0000,,And it did.