0:00:00.228,0:00:04.714
Lets see if we can express 16 over 21 as an decimal

0:00:04.852,0:00:06.355
Or we can call this sixteen twenty first.

0:00:06.370,0:00:09.185
This is also sixteen divided by 21.

0:00:09.339,0:00:12.610
So we can literally just divide 21 into 16.

0:00:12.718,0:00:14.582
And because 21 is larger than 16,

0:00:14.613,0:00:17.301
we're going to get something less than 1.

0:00:17.424,0:00:22.113
So let's just literally divide 21 into 16.

0:00:22.205,0:00:25.282
And we we're going to have some less than one, so lets add some decimal places here.

0:00:25.359,0:00:31.216
We're going to round to the nearest thousandths in case our digits just keep going on and on and on.

0:00:31.339,0:00:34.759
And let's start dividing, 21 goes into 1 zero times,

0:00:34.759,0:00:36.724
21 goes into 16 zero times.

0:00:36.832,0:00:41.727
21 goes into 160, well, 20 would go into 160 8 times,

0:00:41.773,0:00:45.859
So let's try 7, lets see if 7 is the right thing.

0:00:46.166,0:00:52.524
7 times 1 is 7, 7 times 2 is 14 and then when we subtract,

0:00:52.678,0:00:54.529
we should get a remainder less than 21.

0:00:54.559,0:00:59.562
If we picked the largest number here that goes into the largest number here,

0:00:59.686,0:01:03.651
that if I multiply it by 21 I get close to 160 without going over.

0:01:03.682,0:01:07.271
And so if we subtract we do get 13, we do get 13.

0:01:07.348,0:01:10.570
So that worked, 13 is less than 21.

0:01:10.586,0:01:13.240
And you could just subtract, I did it in my head right there,

0:01:13.302,0:01:15.678
but you could re-group, you could say that this is a 10

0:01:15.678,0:01:17.369
and then this would be a 5

0:01:17.430,0:01:18.755
10 minus 7 is 3.

0:01:18.878,0:01:20.105
5 minus 4 is 1,

0:01:20.151,0:01:22.107
1 minus 1 is zero.

0:01:22.214,0:01:25.953
Now lets bring down a zero

0:01:26.122,0:01:30.279
21 goes into 130, so lets see, would 6 work?

0:01:30.587,0:01:31.738
It looks like 6 would work

0:01:31.845,0:01:34.769
6 times 21 is 126, so that looks like it works.

0:01:34.784,0:01:36.665
So lets put a 6 there

0:01:36.695,0:01:38.292
6 times 1 is 6

0:01:38.338,0:01:42.468
6 times 2 is 120. There's a little bit of an art to this.

0:01:42.545,0:01:43.876
Alright, now let's subtract.

0:01:44.015,0:01:45.421
Once again, we can regroup,

0:01:45.483,0:01:48.290
this would be a 10, we've taken 10 from

0:01:48.290,0:01:50.716
essentially this 30, so this becomes a 2

0:01:50.808,0:01:53.152
10 minus six is 4

0:01:53.352,0:01:54.541
2 minus 2 is zero

0:01:54.618,0:01:56.138
1 minus 1 is zero.

0:01:56.199,0:02:00.329
Now let's bring down, now lets bring down another zero

0:02:00.329,0:02:03.791
21 goes into 40, well, almost 2 times

0:02:03.930,0:02:06.116
but not quite, so only 1 time.

0:02:06.301,0:02:09.762
1 times 21 is 21, and now lets subtract

0:02:09.839,0:02:12.269
This is a 10, this becomes a 3.

0:02:12.330,0:02:14.239
10 minus 1 is 9

0:02:14.531,0:02:17.885
3 minus 2 is 1 and we're going to have get

0:02:17.885,0:02:21.315
this digit because we want to round to the nearest thousand.

0:02:21.376,0:02:24.572
So if this is 5 or over we're going to round up

0:02:24.633,0:02:28.084
if this is less than 5 we're going to round down.

0:02:28.192,0:02:30.152
So let's bring another 0, lets bring another

0:02:30.182,0:02:32.974
lets bring another zero down here

0:02:33.036,0:02:38.098
and 21 goes into 190, lets see I think 9 will work

0:02:38.436,0:02:41.135
Lets try 9, 9 times 1 is 9

0:02:41.243,0:02:49.067
9 times 2 is 18, when you subtract 190 minus 189 is 1

0:02:49.343,0:02:52.913
And we could keep going on and on but we already have

0:02:52.959,0:02:54.925
enough digits to round to the nearest thousand.

0:02:55.017,0:02:57.911
This digit right over here is greater than

0:02:58.126,0:03:01.387
this is greater than or equal to 5, so we will round up

0:03:01.602,0:03:03.957
in the thousandths place.

0:03:04.141,0:03:05.808
So if we round to the nearest thousandths,

0:03:05.993,0:03:09.370
we can say that this is 0.76

0:03:09.523,0:03:14.400
and then this where we're going to round up, 762.