WEBVTT mathematics/basic-math/pyo
00:00:00.000 --> 00:00:06.800
Welcome back to Educator.com; this lesson is on rounding decimals.
00:00:06.800 --> 00:00:11.700
To begin, we need to go over the place values.
00:00:11.700 --> 00:00:30.200
If I have a number right here, 12,345 and 6679 ten thousandths, each number has a place value.
00:00:30.200 --> 00:00:33.000
The 1 right here is ten thousands.
00:00:33.000 --> 00:00:41.600
The 2, the one right before the comma, thousands; this is hundreds, tens, ones.
00:00:41.600 --> 00:00:48.100
The important part is looking at the numbers after the decimal point.
00:00:48.100 --> 00:00:51.400
The decimal point is read as AND.
00:00:51.400 --> 00:00:55.800
6, this first number is not one'ths; it is actually tenths.
00:00:55.800 --> 00:01:01.200
It starts off as the tenths value with a -TH.
00:01:01.200 --> 00:01:09.900
The next one would be hundredths, thousandths, ten thousandths; keep this in mind.
00:01:09.900 --> 00:01:18.900
Make sure you look over this and remember these place values.
00:01:18.900 --> 00:01:25.300
When we round decimals, the first thing you are going to do is circle...
00:01:25.300 --> 00:01:33.900
You don't have to circle--but it just makes it easier--the number in the place value that you have to round to.
00:01:33.900 --> 00:01:38.700
If you look at this example right here, it says this number to the nearest tenth.
00:01:38.700 --> 00:01:42.700
I know that tenths is the first number after the decimal point.
00:01:42.700 --> 00:01:50.800
I am going to take that; I am going to circle that number, 5.
00:01:50.800 --> 00:02:02.900
Look at the number after the circled number; behind; the number behind is a 6.
00:02:02.900 --> 00:02:07.600
That number behind the circled number, if it is greater than 5,
00:02:07.600 --> 00:02:12.400
5 or greater, then you add one to the circled number,
00:02:12.400 --> 00:02:15.100
meaning you are going to round that number up.
00:02:15.100 --> 00:02:22.900
If it is smaller than 5--4, 3, 2, 1, or 0--then you don't make any changes to that circled number.
00:02:22.900 --> 00:02:24.400
You keep it as a 5.
00:02:24.400 --> 00:02:26.900
This circled number is either going to stay a 5.
00:02:26.900 --> 00:02:32.400
Or it is going to become a 6 if you round up.
00:02:32.400 --> 00:02:38.500
After you determine that, you are going to rewrite the number, the whole number, the whole thing,
00:02:38.500 --> 00:02:44.500
but replace all the numbers behind the circled number with 0s.
00:02:44.500 --> 00:02:47.900
That is the point of rounding; you are going to stop at this number.
00:02:47.900 --> 00:02:49.400
That is going to be the last number you are going to write.
00:02:49.400 --> 00:02:53.900
The rest are going to become zeros.
00:02:53.900 --> 00:02:58.700
This number 6, the number behind the circled number, is greater than 5
00:02:58.700 --> 00:03:04.100
which means I have to take this circled number and round it up.
00:03:04.100 --> 00:03:06.800
I am going to add 1 to the circled number.
00:03:06.800 --> 00:03:15.700
This number is going to become a 6; this number is now a 6.
00:03:15.700 --> 00:03:23.500
I am going to rewrite all the numbers, the whole thing, but replace the last numbers with 0s.
00:03:23.500 --> 00:03:38.700
My new number, after rounding, it is going to become 1 thousand 2 hundred and 34 and 6 tenths.
00:03:38.700 --> 00:03:43.300
Then I can put 0s at the end of them.
00:03:43.300 --> 00:03:48.900
This is my new number, my rounded number.
00:03:48.900 --> 00:03:52.000
Let's do a few more example; round each.
00:03:52.000 --> 00:04:01.600
Here is the number; this is read 4 hundred 26 and 93 hundredths.
00:04:01.600 --> 00:04:07.800
This number right here, 93, you read it as a hundredths because that is the last number that you see there.
00:04:07.800 --> 00:04:12.200
That is the last place value; this is tenths; this is hundredths.
00:04:12.200 --> 00:04:16.500
You are going to read this as 93 hundredths.
00:04:16.500 --> 00:04:23.200
It says to round this to the nearest tenths... sorry, tens.
00:04:23.200 --> 00:04:30.100
The tens... number the tens value; this is ones; this is tens.
00:04:30.100 --> 00:04:35.500
I am going to circle that; the number behind it is a 6.
00:04:35.500 --> 00:04:38.300
It is greater than 5.
00:04:38.300 --> 00:04:45.100
The 6 value is greater than 5 which means the circled number becomes a 3.
00:04:45.100 --> 00:04:50.900
I have to round up by adding 1.
00:04:50.900 --> 00:04:54.400
All the numbers before the 2 stay the same.
00:04:54.400 --> 00:04:58.500
The numbers behind the 2 are replaced with 0s.
00:04:58.500 --> 00:05:04.100
Don't forget the decimal though; you still have to have that decimal.
00:05:04.100 --> 00:05:09.400
This number is before the 2; so 4.
00:05:09.400 --> 00:05:13.100
The circled number... again remember we were going to round up.
00:05:13.100 --> 00:05:23.000
That becomes a 3; the 6 becomes a 0; everything else becomes 0s.
00:05:23.000 --> 00:05:32.500
If I round to the nearest tens, then this number is going to become 430 or 430.00.
00:05:32.500 --> 00:05:39.400
The next one; round to the nearest tenths; the tenths.
00:05:39.400 --> 00:05:43.000
Be careful, the tenths is the first number after the decimal point.
00:05:43.000 --> 00:05:47.700
That is this 0; 0.
00:05:47.700 --> 00:05:49.900
Then I look at the number right behind it which is a 9.
00:05:49.900 --> 00:05:56.700
It is greater than 5; my zero rounds up.
00:05:56.700 --> 00:06:11.700
I do 31 point ...0 becomes a 1; everything else becomes 0.
00:06:11.700 --> 00:06:17.100
The next few examples; we have this number right here to the nearest hundredths.
00:06:17.100 --> 00:06:23.400
Tenths, hundredths; circle this number; I look at the number behind it.
00:06:23.400 --> 00:06:26.300
Is it 5 or greater?--yes it is.
00:06:26.300 --> 00:06:31.600
That means this 2 rounds up to become a 3.
00:06:31.600 --> 00:06:39.100
All the numbers before it stay the same, 22.8.
00:06:39.100 --> 00:06:41.900
Instead of writing the 2, I have to write the 3.
00:06:41.900 --> 00:06:47.900
The numbers behind it become 0s; that is my answer.
00:06:47.900 --> 00:06:53.000
The next one, round this to the nearest hundredths again.
00:06:53.000 --> 00:06:59.800
Hundredths... tenths, hundredths; circle it.
00:06:59.800 --> 00:07:03.900
The number after it, the number behind it is a 3.
00:07:03.900 --> 00:07:11.700
That is not 5 or greater; it is smaller than 5 which means my 6 stays the same.
00:07:11.700 --> 00:07:15.400
If it is smaller than 5, the number behind it, this number right here,
00:07:15.400 --> 00:07:21.200
if it is smaller than 5, then I don't make any changes to that 6.
00:07:21.200 --> 00:07:26.300
I don't subtract 1; I just leave it the same.
00:07:26.300 --> 00:07:31.700
It is either going to be the same; or you are going to add 1 to it.
00:07:31.700 --> 00:07:47.300
It is 44 and 96 hundredths; and then 00.
00:07:47.300 --> 00:07:48.900
This number to the nearest tenths.
00:07:48.900 --> 00:07:54.100
The tenths is again this number right here, the first number after the decimal point.
00:07:54.100 --> 00:07:58.200
Look at the number behind it; is the number behind it 5 or greater?
00:07:58.200 --> 00:08:00.900
Yes, it is 5 or greater; it is 5.
00:08:00.900 --> 00:08:07.500
I have to add 1 to that circled number; this becomes a 1 now.
00:08:07.500 --> 00:08:18.300
693 and 1 tenths; I can put these as 0s.
00:08:18.300 --> 00:08:23.400
The next, nearest tens.
00:08:23.400 --> 00:08:30.100
The difference between this one and this one--tenths, tens; this one has the -TH.
00:08:30.100 --> 00:08:34.300
That means it is this place value right here after the decimal point.
00:08:34.300 --> 00:08:40.700
Tens would be this number right here because it is ones and tens.
00:08:40.700 --> 00:08:43.500
I look at the number right behind it.
00:08:43.500 --> 00:08:52.700
It is smaller than 5 which means my circled number stays the same.
00:08:52.700 --> 00:09:06.700
This would be 60 or 69; my 3 changes to a 0, decimal point, 000.
00:09:06.700 --> 00:09:12.600
Keep in mind, when you have 0s at the end of a number
00:09:12.600 --> 00:09:16.800
after the decimal point, then I don't have to write them out.
00:09:16.800 --> 00:09:23.000
Again only the 0s that are at the end of a number and behind the decimal point.
00:09:23.000 --> 00:09:31.000
In that case, I don't have to write them; you could; you don't have to.
00:09:31.000 --> 00:09:35.100
If there is a 0 before the decimal point, in front of it,
00:09:35.100 --> 00:09:41.500
then you have to because 69 we know is different than 690.
00:09:41.500 --> 00:09:43.800
You have to make sure to have that 0 there.
00:09:43.800 --> 00:09:47.300
But these 0s, as long as they are at the end of a number,
00:09:47.300 --> 00:09:52.200
and it is behind the decimal point, then you don't have to write them out.
00:09:52.200 --> 00:09:59.700
But you could; you could just leave it like this; this is fine.
00:09:59.700 --> 00:10:04.200
This number to the nearest thousands; no -TH.
00:10:04.200 --> 00:10:13.600
That means that the thousands is the number right before the first comma.
00:10:13.600 --> 00:10:16.500
Right in front of the first comma is the thousands.
00:10:16.500 --> 00:10:18.600
I am going to circle that.
00:10:18.600 --> 00:10:21.800
The number before it is a 5; it is 5 or greater.
00:10:21.800 --> 00:10:29.700
That means I have to change this 0 to a 1.
00:10:29.700 --> 00:10:36.500
I am going to write all the numbers before it--1, 8, 9.
00:10:36.500 --> 00:10:42.800
Instead of writing the 0, I am going to write the 1; write my commas.
00:10:42.800 --> 00:10:50.900
Remember all the numbers after the circled number are going to turn into 0s.
00:10:50.900 --> 00:10:54.500
This was my circled number; that changed to a 1; 0 to 1.
00:10:54.500 --> 00:10:59.500
It is going to become 000.00.
00:10:59.500 --> 00:11:03.000
Again because these 0s are at the end of a number,
00:11:03.000 --> 00:11:06.000
and they are behind the decimal point, I don't have to write them out.
00:11:06.000 --> 00:11:10.800
But I could if I want; I could just leave it like that.
00:11:10.800 --> 00:11:18.000
This is the number when you round this to the nearest thousands.
00:11:18.000 --> 00:11:23.500
Now this one is to the nearest thousandths with a -TH.
00:11:23.500 --> 00:11:31.000
We know it is behind the decimal point; here is tenths, hundredths, thousandths.
00:11:31.000 --> 00:11:34.800
I am going to round to that number and circle it.
00:11:34.800 --> 00:11:37.300
Look at the number behind it; it is a 7.
00:11:37.300 --> 00:11:41.400
It is 5 or greater; 7 is bigger than 5.
00:11:41.400 --> 00:11:47.000
That means I change the circled number to a 5; I round up.
00:11:47.000 --> 00:11:54.900
Again the circled number, it is either going to stay the same if this number behind it is smaller than 5.
00:11:54.900 --> 00:12:01.100
Or it is going to become 1 bigger if the number behind it is 5 or greater.
00:12:01.100 --> 00:12:07.100
When I rewrite my number, I am going to write all the numbers in front of it up to my circled number.
00:12:07.100 --> 00:12:26.000
All the numbers behind it becomes 0s; 5.055; this becomes 0 right there.
00:12:26.000 --> 00:12:31.000
That is it for this lesson on rounding decimals; thank you for watching Educator.com.