0:00:00.200,0:00:00.700
Welcome to the presentation on ordering numbers.

0:00:00.700,0:00:06.940
Let's get started with some problems that I think,

0:00:06.940,0:00:09.270
as you go through the examples,

0:00:09.270,0:00:10.910
hopefully you'll understand how to do these problems.

0:00:10.910,0:00:11.700
So let's see.

0:00:11.700,0:00:23.200
The first set of numbers that we have to order is thirty-five point seven percent,

0:00:23.200,0:00:44.590
one hundred eight point one percent, zero point five, thirteen over ninety-three, one, and seven over sixty-eight.

0:00:44.590,0:00:46.590
So let's do this problem.

0:00:46.590,0:00:48.810
The important thing to remember whenever you're doing this type of ordering of numbers

0:00:48.810,0:00:52.820
is to realize that these are all just different ways to represent--

0:00:52.820,0:00:56.940
these are all a percent or a decimal or a fraction or a mixed--

0:00:56.940,0:01:00.270
are all just different ways of representing numbers.

0:01:02.680,0:01:05.110
It's very hard to compare when you just look at it like this,

0:01:05.110,0:01:07.130
so what I like to do is I like to convert them all to decimals.

0:01:08.190,0:01:11.100
But there could be someone who likes to convert them all to percentages,

0:01:11.100,0:01:14.220
or convert them all to fractions and then compare.

0:01:14.220,0:01:16.920
But I always find decimals to be the easiest way to compare.

0:01:16.920,0:01:19.370
So let's start with this thirty-five point seven percent.

0:01:19.370,0:01:21.940
Let's turn this into a decimal.

0:01:21.940,0:01:25.090
Well, the easiest thing to remember is if you have a percent,

0:01:25.090,0:01:27.490
you just get rid of the percent sign and put it over one hundred.

0:01:28.580,0:01:38.970
So thirty-five point seven percent is the same thing as thirty-five point seven over one hundred.

0:01:38.970,0:01:43.020
Like five percent, that's the same thing as five over one hundred,

0:01:43.020,0:01:45.050
or fifty percent is just the same thing as fifty over one hundred.

0:01:45.050,0:01:53.990
So thirty-five point seven over one hundred, well, that[br]just equals zero point three five seven.

0:01:53.990,0:01:55.730
If this got you a little confused,

0:01:55.730,0:02:01.970
another way to think about percentage points is if I write thirty-five point seven percent,

0:02:01.970,0:02:05.540
all you have to do is get rid of the percent sign and move the decimal to the left two spaces,

0:02:05.540,0:02:10.140
and it becomes zero point three five seven.

0:02:10.140,0:02:11.870
Let me give you a couple of more examples down here.

0:02:11.870,0:02:16.050
Let's say I had five percent.

0:02:16.050,0:02:20.020
That is the same thing as five over one hundred.

0:02:20.020,0:02:22.670
Or if you do the decimal technique, five percent,

0:02:22.670,0:02:24.730
you could just move the decimal and you get rid of the percent.

0:02:24.730,0:02:28.630
And you move the decimal over one and two, and you put a zero here.

0:02:28.630,0:02:30.370
It's zero point zero five.

0:02:30.370,0:02:33.280
And that's the same thing as zero point zero five.

0:02:33.280,0:02:36.380
You also know that zero point zero five and five over one hundred are the same thing.

0:02:36.380,0:02:37.620
So let's get back to the problem.

0:02:37.620,0:02:40.772
I hope that distraction didn't distract you too much.

0:02:40.772,0:02:43.190
Let me scratch out all this.

0:02:43.190,0:02:49.050
So thirty-five point seven percent is equal to zero point three five seven.

0:02:49.050,0:02:51.870
Similarly, one hundred eight point one percent--

0:02:51.870,0:02:54.080
Let's to the technique where we[br]just get rid of the percent and

0:02:54.080,0:02:59.350
move the decimal space over[br]1, 2 spaces to the left.

0:02:59.350,0:03:08.600
So then that equals 1.081.

0:03:08.600,0:03:11.570
See we already know that[br]this is smaller than this.

0:03:11.570,0:03:14.140
Well the next one is easy,[br]it's already in decimal form.

0:03:14.140,0:03:16.040
0.5 is just going to[br]be equal to 0.5.

0:03:16.040,0:03:18.820
[br]Now 13/93.

0:03:21.050,0:03:24.340
To convert a fraction into[br]a decimal we just take the

0:03:24.340,0:03:27.320
denominator and divide[br]it into the numerator.

0:03:27.320,0:03:29.350
So let's do that.

0:03:29.350,0:03:33.020
93 goes into 13?

0:03:34.775,0:03:36.530
[br]Well, we know it goes[br]into 13 zero times.

0:03:39.760,0:03:43.990
So let's add a[br]decimal point here.

0:03:43.990,0:03:47.550
So how many times[br]does 93 go into 130?

0:03:47.550,0:03:49.530
Well, it goes into it one time.

0:03:49.530,0:03:51.564
1 times 93 is 93.

0:03:55.364,0:03:56.569
Becomes a 10.

0:03:56.673,0:03:58.637
That becomes a 2.

0:03:58.960,0:04:03.700
Then we're going to[br]borrow, so get 37.

0:04:03.700,0:04:06.590
Bring down a 0.

0:04:06.590,0:04:10.010
So 93 goes into 370?

0:04:10.010,0:04:10.470
Let's see.

0:04:10.470,0:04:14.790
4 times 93 would be 372,[br]so it actually goes into

0:04:14.790,0:04:15.695
it only three times.

0:04:15.695,0:04:19.390
[br]3 times 3 is 9.

0:04:22.880,0:04:25.270
3 times 9 is 27.

0:04:25.270,0:04:30.110
[br]So this equals?

0:04:31.605,0:04:38.050
Let's see, this equals-- if we[br]say that this 0 becomes a 10.

0:04:38.050,0:04:39.620
This become a 16.

0:04:39.620,0:04:42.440
This becomes a 2.

0:04:42.440,0:04:45.210
81.

0:04:45.210,0:04:48.120
And then we say, how many[br]times does 93 go into 810?

0:04:48.120,0:04:50.860
It goes roughly 8 times.

0:04:50.860,0:04:52.860
And we could actually keep[br]going, but for the sake of

0:04:52.860,0:04:55.640
comparing these numbers, we've[br]already gotten to a pretty

0:04:55.640,0:04:57.580
good level of accuracy.

0:04:57.580,0:05:00.740
So let's just stop this problem[br]here because the decimal

0:05:00.740,0:05:02.720
numbers could keep going on,[br]but for the sake of comparison

0:05:02.720,0:05:04.410
I think we've already got a[br]good sense of what this

0:05:04.410,0:05:05.360
decimal looks like.

0:05:05.360,0:05:10.330
It's 0.138 and then[br]it'll just keep going.

0:05:10.330,0:05:13.010
So let's write that down.

0:05:13.010,0:05:15.340
And then finally, we have[br]this mixed number here.

0:05:15.340,0:05:18.070
And let me erase some of[br]my work because I don't

0:05:18.070,0:05:18.840
want to confuse you.

0:05:18.840,0:05:22.700
Actually, let me keep it[br]the way it is right now.

0:05:22.700,0:05:26.120
The easiest way to convert a[br]mixed number into a decimal is

0:05:26.120,0:05:29.630
to just say, OK, this is 1[br]and then some fraction

0:05:29.630,0:05:32.920
that's less than 1.

0:05:32.920,0:05:36.420
Or we could convert it to a[br]fraction, an improper fraction

0:05:36.420,0:05:38.790
like-- oh, actually there are[br]no improper fractions here.

0:05:38.790,0:05:39.640
Actually, let's do it that way.

0:05:39.640,0:05:41.630
Let's convert to an improper[br]fraction and then convert

0:05:41.630,0:05:44.110
that into a decimal.

0:05:44.110,0:05:46.060
Actually, I think I'm going to[br]need more space, so let me

0:05:46.060,0:05:48.740
clean up this a little bit.

0:05:48.740,0:05:58.240
[br]There.

0:05:58.595,0:06:01.040
We have a little more[br]space to work with now.

0:06:01.040,0:06:04.260
So 1 and 7/68.

0:06:08.570,0:06:13.700
So to go from a mixed number to[br]an improper fraction, what you

0:06:13.700,0:06:18.760
do is you take the 68 times 1[br]and add it to the

0:06:18.760,0:06:19.720
numerator here.

0:06:26.120,0:06:29.680
1 and 7/68 is the same[br]thing as 1 plus 7/68.

0:06:29.680,0:06:32.800
And that's the same thing as[br]you know from the fractions

0:06:32.800,0:06:40.330
module, as 68/68 plus 7/68.

0:06:40.330,0:06:47.650
And that's the same thing[br]as 68 plus 7-- 75/68.

0:06:47.650,0:06:51.790
So 1 and 7/68 is[br]equal to 75/68.

0:06:51.790,0:06:54.870
And now we convert this to a[br]decimal using the technique

0:06:54.870,0:06:56.350
we did for 13/93.

0:06:56.350,0:06:58.570
So we say-- let me[br]get some space.

0:07:07.360,0:07:09.160
68 goes into 75 one time.

0:07:09.160,0:07:13.290
1 times 68 is 68.

0:07:13.290,0:07:16.460
75 minus 68 is 7.

0:07:16.460,0:07:17.350
Bring down the 0.

0:07:17.350,0:07:20.490
Actually, you don't have to[br]write the decimal there.

0:07:20.490,0:07:21.100
Ignore that decimal.

0:07:21.100,0:07:24.400
68 goes into 70 one time.

0:07:24.400,0:07:28.150
1 times 68 is 68.

0:07:28.150,0:07:30.990
70 minus 68 is 2,[br]bring down another 0.

0:07:30.990,0:07:33.240
68 goes into 20 zero times.

0:07:33.240,0:07:36.550
And the problem's going to keep[br]going on, but I think we've

0:07:36.550,0:07:38.990
already once again, gotten to[br]enough accuracy that

0:07:38.990,0:07:40.040
we can compare.

0:07:40.040,0:07:48.320
So 1 and 7/68 we've now figured[br]out is equal to 1.10 -- and if we kept dividing we'd get more decimals of accuracy. So we're ready to compare.

0:07:53.510,0:07:56.550
So all of these numbers I just[br]rewrote them as decimals.

0:07:56.550,0:08:00.550
So 35.7% is 0.357.

0:08:05.720,0:08:09.660
It's 108.1% is equal to 1.081.

0:08:09.660,0:08:11.260
0.5 is 0.5.

0:08:11.260,0:08:15.770
13/93 is 0.138.

0:08:15.770,0:08:20.850
And 1 and 7/68 is 1.10[br]and it'll keep going on.

0:08:20.850,0:08:23.010
So what's the smallest?

0:08:23.010,0:08:26.320
So the smallest is . -- actually, no.

0:08:26.320,0:08:28.300
The smallest is right here.

0:08:28.300,0:08:31.450
So I'm going to rank them[br]from smallest to largest.

0:08:31.450,0:08:36.250
So the smallest is 0.138.

0:08:36.250,0:08:40.640
Then the next largest[br]is going to be 0.357. Right?

0:08:40.640,0:08:44.470
Then the next largest[br]is going to be 0.5.

0:08:44.470,0:08:47.460
Then you're going to have 1.08.

0:08:47.460,0:08:54.620
And then you're going[br]to have 1 and 7/68.

0:08:54.620,0:08:56.840
Well, actually, I'm going to do[br]more examples of this, but for

0:08:56.840,0:08:59.890
this video I think this is the[br]only one I have time for.

0:08:59.890,0:09:01.910
But hopefully this gives you a[br]sense of doing these problems.

0:09:01.910,0:09:04.370
I always find it easier[br]to go into the decimal

0:09:04.370,0:09:05.280
mode to compare.

0:09:05.280,0:09:06.680
And actually, the hints[br]on the module will

0:09:06.680,0:09:08.670
be the same for you.

0:09:08.670,0:09:11.040
But I think you're ready at[br]least now to try the problems.

0:09:11.040,0:09:13.170
If you're not, if you want to[br]see other examples, you might

0:09:13.170,0:09:16.830
just want to either re-watch[br]this video and/or I might

0:09:16.830,0:09:20.530
record some more videos with[br]more examples right now.

0:09:20.530,0:09:22.560
Anyway, have fun.