0:00:00.890,0:00:03.770
I'll now show you how[br]to convert a fraction

0:00:03.770,0:00:04.920
into a decimal.

0:00:04.920,0:00:06.990
And if we have time, maybe[br]we'll learn how to do a

0:00:06.990,0:00:08.730
decimal into a fraction.

0:00:08.730,0:00:11.420
So let's start with, what[br]I would say, is a fairly

0:00:11.420,0:00:12.480
straightforward example.

0:00:12.480,0:00:15.210
Let's start with[br]the fraction 1/2.

0:00:15.210,0:00:17.390
And I want to convert[br]that into a decimal.

0:00:17.390,0:00:20.170
So the method I'm going to[br]show you will always work.

0:00:20.170,0:00:22.850
What you do is you take the[br]denominator and you divide

0:00:22.850,0:00:24.530
it into the numerator.

0:00:24.530,0:00:25.510
Let's see how that works.

0:00:25.510,0:00:29.110
So we take the denominator-- is[br]2-- and we're going to divide

0:00:29.110,0:00:32.280
that into the numerator, 1.

0:00:32.280,0:00:34.110
And you're probably saying,[br]well, how do I divide 2 into 1?

0:00:34.110,0:00:37.010
Well, if you remember from the[br]dividing decimals module, we

0:00:37.010,0:00:40.220
can just add a decimal point[br]here and add some trailing 0's.

0:00:40.220,0:00:42.880
We haven't actually changed the[br]value of the number, but we're

0:00:42.880,0:00:45.260
just getting some[br]precision here.

0:00:45.260,0:00:46.700
We put the decimal point here.

0:00:50.260,0:00:50.650
Does 2 go into 1?

0:00:50.650,0:00:51.280
No.

0:00:51.280,0:00:56.180
2 goes into 10, so we go 2[br]goes into 10 five times.

0:00:56.180,0:00:59.060
5 times 2 is 10.

0:00:59.060,0:01:00.050
Remainder of 0.

0:01:00.050,0:01:01.150
We're done.

0:01:01.150,0:01:06.675
So 1/2 is equal to 0.5.

0:01:10.570,0:01:12.050
Let's do a slightly harder one.

0:01:12.050,0:01:15.000
Let's figure out 1/3.

0:01:15.000,0:01:19.190
Well, once again, we take the[br]denominator, 3, and we divide

0:01:19.190,0:01:20.740
it into the numerator.

0:01:20.740,0:01:25.470
And I'm just going to add a[br]bunch of trailing 0's here.

0:01:25.470,0:01:27.800
3 goes into-- well, 3[br]doesn't go into 1.

0:01:27.800,0:01:30.150
3 goes into 10 three times.

0:01:30.150,0:01:32.452
3 times 3 is 9.

0:01:32.452,0:01:35.720
Let's subtract, get a[br]1, bring down the 0.

0:01:35.720,0:01:37.700
3 goes into 10 three times.

0:01:37.700,0:01:39.700
Actually, this decimal[br]point is right here.

0:01:39.700,0:01:42.710
3 times 3 is 9.

0:01:42.710,0:01:43.930
Do you see a pattern here?

0:01:43.930,0:01:45.070
We keep getting the same thing.

0:01:45.070,0:01:47.350
As you see it's[br]actually 0.3333.

0:01:47.350,0:01:48.830
It goes on forever.

0:01:48.830,0:01:52.160
And a way to actually represent[br]this, obviously you can't write

0:01:52.160,0:01:54.020
an infinite number of 3's.

0:01:54.020,0:02:00.430
Is you could just write 0.--[br]well, you could write 0.33

0:02:00.430,0:02:03.060
repeating, which means that[br]the 0.33 will go on forever.

0:02:03.060,0:02:06.960
Or you can actually even[br]say 0.3 repeating.

0:02:06.960,0:02:08.630
Although I tend to[br]see this more often.

0:02:08.630,0:02:09.840
Maybe I'm just mistaken.

0:02:09.840,0:02:12.410
But in general, this line on[br]top of the decimal means

0:02:12.410,0:02:17.320
that this number pattern[br]repeats indefinitely.

0:02:17.320,0:02:25.210
So 1/3 is equal to 0.33333[br]and it goes on forever.

0:02:25.210,0:02:29.770
Another way of writing[br]that is 0.33 repeating.

0:02:29.770,0:02:33.400
Let's do a couple of, maybe a[br]little bit harder, but they

0:02:33.400,0:02:35.060
all follow the same pattern.

0:02:35.060,0:02:36.890
Let me pick some weird numbers.

0:02:40.470,0:02:41.890
Let me actually do an[br]improper fraction.

0:02:41.890,0:02:49.050
Let me say 17/9.

0:02:49.050,0:02:50.160
So here, it's interesting.

0:02:50.160,0:02:52.260
The numerator is bigger[br]than the denominator.

0:02:52.260,0:02:54.200
So actually we're going to[br]get a number larger than 1.

0:02:54.200,0:02:55.270
But let's work it out.

0:02:55.270,0:03:00.586
So we take 9 and we[br]divide it into 17.

0:03:00.586,0:03:06.000
And let's add some trailing 0's[br]for the decimal point here.

0:03:06.000,0:03:08.730
So 9 goes into 17 one time.

0:03:08.730,0:03:11.260
1 times 9 is 9.

0:03:11.260,0:03:14.040
17 minus 9 is 8.

0:03:14.040,0:03:16.240
Bring down a 0.

0:03:16.240,0:03:20.080
9 goes into 80-- well, we know[br]that 9 times 9 is 81, so it has

0:03:20.080,0:03:21.830
to go into it only eight times[br]because it can't go

0:03:21.830,0:03:23.230
into it nine times.

0:03:23.230,0:03:27.010
8 times 9 is 72.

0:03:27.010,0:03:29.560
80 minus 72 is 8.

0:03:29.560,0:03:30.770
Bring down another 0.

0:03:30.770,0:03:32.260
I think we see a[br]pattern forming again.

0:03:32.260,0:03:35.990
9 goes into 80 eight times.

0:03:35.990,0:03:40.820
8 times 9 is 72.

0:03:40.820,0:03:44.350
And clearly, I could keep[br]doing this forever and

0:03:44.350,0:03:46.790
we'd keep getting 8's.

0:03:46.790,0:03:53.740
So we see 17 divided by 9 is[br]equal to 1.88 where the 0.88

0:03:53.740,0:03:56.080
actually repeats forever.

0:03:56.080,0:03:59.200
Or, if we actually wanted to[br]round this we could say that

0:03:59.200,0:04:01.430
that is also equal to 1.--[br]depending where we wanted

0:04:01.430,0:04:02.860
to round it, what place.

0:04:02.860,0:04:05.990
We could say roughly 1.89.

0:04:05.990,0:04:07.480
Or we could round in[br]a different place.

0:04:07.480,0:04:09.310
I rounded in the 100's place.

0:04:09.310,0:04:11.350
But this is actually[br]the exact answer.

0:04:11.350,0:04:15.126
17/9 is equal to 1.88.

0:04:15.126,0:04:17.380
I actually might do a separate[br]module, but how would we write

0:04:17.380,0:04:20.730
this as a mixed number?

0:04:20.730,0:04:23.030
Well actually, I'm going[br]to do that in a separate.

0:04:23.030,0:04:24.390
I don't want to[br]confuse you for now.

0:04:24.390,0:04:25.380
Let's do a couple[br]more problems.

0:04:28.560,0:04:29.980
Let me do a real weird one.

0:04:29.980,0:04:34.360
Let me do 17/93.

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What does that equal[br]as a decimal?

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Well, we do the same thing.

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93 goes into-- I make a really[br]long line up here because

0:04:45.630,0:04:47.930
I don't know how many[br]decimal places we'll do.

0:04:50.570,0:04:53.220
And remember, it's always the[br]denominator being divided

0:04:53.220,0:04:54.930
into the numerator.

0:04:54.930,0:04:56.950
This used to confuse me a lot[br]of times because you're often

0:04:56.950,0:04:59.630
dividing a larger number[br]into a smaller number.

0:04:59.630,0:05:02.580
So 93 goes into 17 zero times.

0:05:02.580,0:05:04.080
There's a decimal.

0:05:04.080,0:05:05.990
93 goes into 170?

0:05:05.990,0:05:07.270
Goes into it one time.

0:05:07.270,0:05:11.410
1 times 93 is 93.

0:05:11.410,0:05:14.370
170 minus 93 is 77.

0:05:17.980,0:05:20.360
Bring down the 0.

0:05:20.360,0:05:23.700
93 goes into 770?

0:05:23.700,0:05:24.660
Let's see.

0:05:24.660,0:05:29.120
It will go into it, I think,[br]roughly eight times.

0:05:29.120,0:05:33.330
8 times 3 is 24.

0:05:33.330,0:05:35.970
8 times 9 is 72.

0:05:35.970,0:05:39.730
Plus 2 is 74.

0:05:39.730,0:05:42.186
And then we subtract.

0:05:42.186,0:05:43.990
10 and 6.

0:05:43.990,0:05:46.710
It's equal to 26.

0:05:46.710,0:05:47.760
Then we bring down another 0.

0:05:47.760,0:05:52.800
93 goes into 26--[br]about two times.

0:05:52.800,0:05:57.020
2 times 3 is 6.

0:05:57.020,0:05:58.704
18.

0:05:58.704,0:05:59.920
This is 74.

0:06:03.120,0:06:03.930
0.

0:06:03.930,0:06:06.380
So we could keep going.

0:06:06.380,0:06:08.030
We could keep figuring[br]out the decimal points.

0:06:08.030,0:06:10.020
You could do this indefinitely.

0:06:10.020,0:06:12.090
But if you wanted to at least[br]get an approximation, you would

0:06:12.090,0:06:23.490
say 17 goes into 93 0.-- or[br]17/93 is equal to 0.182 and

0:06:23.490,0:06:25.020
then the decimals[br]will keep going.

0:06:25.020,0:06:27.170
And you can keep doing[br]it if you want.

0:06:27.170,0:06:28.650
If you actually saw this on[br]exam they'd probably tell

0:06:28.650,0:06:29.640
you to stop at some point.

0:06:29.640,0:06:31.650
You know, round it to the[br]nearest hundredths or

0:06:31.650,0:06:33.610
thousandths place.

0:06:33.610,0:06:36.550
And just so you know, let's try[br]to convert it the other way,

0:06:36.550,0:06:37.830
from decimals to fractions.

0:06:37.830,0:06:40.090
Actually, this is, I[br]think, you'll find a

0:06:40.090,0:06:42.300
much easier thing to do.

0:06:42.300,0:06:49.810
If I were to ask you what[br]0.035 is as a fraction?

0:06:49.810,0:06:56.845
Well, all you do is you say,[br]well, 0.035, we could write it

0:06:56.845,0:07:05.130
this way-- we could write[br]that's the same thing as 03--

0:07:05.130,0:07:06.300
well, I shouldn't write 035.

0:07:06.300,0:07:10.700
That's the same[br]thing as 35/1,000.

0:07:10.700,0:07:11.580
And you're probably[br]saying, Sal, how did

0:07:11.580,0:07:14.120
you know it's 35/1000?

0:07:14.120,0:07:18.590
Well because we went to 3--[br]this is the 10's place.

0:07:18.590,0:07:20.230
Tenths not 10's.

0:07:20.230,0:07:21.360
This is hundreths.

0:07:21.360,0:07:23.230
This is the thousandths place.

0:07:23.230,0:07:25.890
So we went to 3 decimals[br]of significance.

0:07:25.890,0:07:29.260
So this is 35 thousandths.

0:07:29.260,0:07:38.650
If the decimal was let's[br]say, if it was 0.030.

0:07:38.650,0:07:40.140
There's a couple of ways[br]we could say this.

0:07:40.140,0:07:42.490
Well, we could say, oh well[br]we got to 3-- we went to

0:07:42.490,0:07:43.570
the thousandths Place.

0:07:43.570,0:07:48.240
So this is the same[br]thing as 30/1,000.

0:07:48.240,0:07:48.610
or.

0:07:48.610,0:07:55.550
We could have also said, well,[br]0.030 is the same thing as

0:07:55.550,0:08:02.710
0.03 because this 0 really[br]doesn't add any value.

0:08:02.710,0:08:05.920
If we have 0.03 then we're only[br]going to the hundredths place.

0:08:05.920,0:08:11.100
So this is the same[br]thing as 3/100.

0:08:11.100,0:08:13.160
So let me ask you, are[br]these two the same?

0:08:16.330,0:08:16.670
Well, yeah.

0:08:16.670,0:08:17.680
Sure they are.

0:08:17.680,0:08:20.065
If we divide both the numerator[br]and the denominator of both of

0:08:20.065,0:08:24.890
these expressions by[br]10 we get 3/100.

0:08:24.890,0:08:26.220
Let's go back to this case.

0:08:26.220,0:08:27.550
Are we done with this?

0:08:27.550,0:08:30.120
Is 35/1,000-- I[br]mean, it's right.

0:08:30.120,0:08:31.660
That is a fraction.

0:08:31.660,0:08:32.584
35/1,000.

0:08:32.584,0:08:35.440
But if we wanted to simplify it[br]even more looks like we could

0:08:35.440,0:08:38.530
divide both the numerator[br]and the denominator by 5.

0:08:38.530,0:08:40.860
And then, just to get[br]it into simplest form,

0:08:40.860,0:08:47.280
that equals 7/200.

0:08:47.280,0:08:51.020
And if we wanted to convert[br]7/200 into a decimal using the

0:08:51.020,0:08:54.150
technique we just did, so we[br]would do 200 goes into

0:08:54.150,0:08:56.120
7 and figure it out.

0:08:56.120,0:09:00.170
We should get 0.035.

0:09:00.170,0:09:02.650
I'll leave that up to[br]you as an exercise.

0:09:02.650,0:09:05.370
Hopefully now you get at least[br]an initial understanding of how

0:09:05.370,0:09:09.320
to convert a fraction into a[br]decimal and maybe vice versa.

0:09:09.320,0:09:11.840
And if you don't, just do[br]some of the practices.

0:09:11.840,0:09:16.990
And I will also try to record[br]another module on this

0:09:16.990,0:09:18.880
or another presentation.

0:09:18.880,0:09:20.090
Have fun with the exercises.