WEBVTT mathematics/basic-math/pyo
00:00:00.000 --> 00:00:07.400
Welcome back to Educator.com; this lesson is on connecting decimals and fractions.
00:00:07.400 --> 00:00:17.400
When we connect fractions to decimals and decimals to fractions, let's think about money.
00:00:17.400 --> 00:00:23.800
For fractions and decimals, I can represent each with a dollar.
00:00:23.800 --> 00:00:29.200
If I have half a dollar, 1/2 is half.
00:00:29.200 --> 00:00:35.000
If I have half a dollar, I have fifty cents.
00:00:35.000 --> 00:00:45.500
Keep in mind that 0.5 is the same thing as 0.50 or 50 cents.
00:00:45.500 --> 00:00:51.500
When the numbers are after the decimal place, I can put as many 0s as I want.
00:00:51.500 --> 00:00:56.100
The number does not change.
00:00:56.100 --> 00:01:05.500
I know that half a dollar is the same as 50 cents or 0.5.
00:01:05.500 --> 00:01:10.000
1/2 would be the same as 0.5.
00:01:10.000 --> 00:01:22.600
If I have 1/4 from a dollar, how can I divide the dollar up into 4 parts?
00:01:22.600 --> 00:01:29.400
4 of what makes a dollar?--the answer is quarters.
00:01:29.400 --> 00:01:33.300
We know that 4 quarters make 1 dollar.
00:01:33.300 --> 00:01:47.100
If I have 1 out of 4 quarters, if I have 1 quarter, then I have 25 cents or 0.25.
00:01:47.100 --> 00:01:50.300
How about this one?
00:01:50.300 --> 00:01:54.900
What would I have if I divide the dollar up into 10 parts?
00:01:54.900 --> 00:01:57.900
I would have 1 dime.
00:01:57.900 --> 00:02:11.600
1/10 would be the same thing as having 1 dime which is 0.1 or 0.10.
00:02:11.600 --> 00:02:16.200
Remember this is the same as this.
00:02:16.200 --> 00:02:18.900
How about this one?
00:02:18.900 --> 00:02:29.400
If I divide up the dollar into 100 parts, then I would have 100 pennies.
00:02:29.400 --> 00:02:40.600
Having 1 of those parts, having 1 penny, is going to be 0.01 or 1 cent.
00:02:40.600 --> 00:02:50.600
1/100 is having 1 cent, 0.01.
00:02:50.600 --> 00:02:56.900
Let's look at this again; this fraction right here, 3/4.
00:02:56.900 --> 00:03:03.300
I am going to again relate it to the fraction 1/4; remember 1/4.
00:03:03.300 --> 00:03:20.000
If I have 1 part out of the 4 that I divided the dollar into, then I have 1 quarter which is 0.25.
00:03:20.000 --> 00:03:23.500
This is the value of 1 quarter.
00:03:23.500 --> 00:03:27.500
If you look at this fraction, this is 3/4.
00:03:27.500 --> 00:03:32.900
The dollar is still divided into 4 parts which is still the quarter.
00:03:32.900 --> 00:03:38.400
If I have 3 quarters, how much do I have?
00:03:38.400 --> 00:03:49.300
I have 0.75 or 75 cents.
00:03:49.300 --> 00:03:56.700
If I want to do this mathematically, I can take the 3 and divide it by 4.
00:03:56.700 --> 00:04:02.200
3, this right here means divide; 3 divided by 4.
00:04:02.200 --> 00:04:09.600
That means I can take 3 divided by 4.
00:04:09.600 --> 00:04:14.500
This is a whole number; I have to put a decimal after it.
00:04:14.500 --> 00:04:22.700
Then I can add as many 0s as I want; let's make this longer.
00:04:22.700 --> 00:04:28.200
4 goes into 3 zero times; I am going to raise up this decimal.
00:04:28.200 --> 00:04:33.100
4 goes into 30 how many times?--let's see.
00:04:33.100 --> 00:04:46.400
4 times 7 is 28; subtract this; this is 2; bring down the 0.
00:04:46.400 --> 00:04:57.000
4 goes into 20 five times.
00:04:57.000 --> 00:05:05.600
If I want to convert 3/4, this fraction into a decimal, I can just do 3 divided by 4.
00:05:05.600 --> 00:05:09.600
I am still going to get the same answer of 0.75.
00:05:09.600 --> 00:05:14.800
But if I know that I can take this and think of the dollar,
00:05:14.800 --> 00:05:19.600
and I know I can divide the dollar into 4 parts which is 4 quarters,
00:05:19.600 --> 00:05:27.600
and I have 3 of those parts, then I have 75 cents.
00:05:27.600 --> 00:05:44.100
Right here, 0.7; 0.7 is the same thing as 0.70.
00:05:44.100 --> 00:05:51.500
0.7 is the same thing as having 70 cents; what gives me 70 cents?
00:05:51.500 --> 00:05:59.500
If I have 7 dimes, then I will have 70 cents.
00:05:59.500 --> 00:06:10.000
Then I can say that this is having 7 over... the value of a dime is 10 cents.
00:06:10.000 --> 00:06:17.000
7/10 would be the same thing as 70 cents.
00:06:17.000 --> 00:06:21.700
If I want to just take this without relating it to the dollar
00:06:21.700 --> 00:06:28.500
and just convert it back to a fraction, I can take this number right here, 7.
00:06:28.500 --> 00:06:31.800
I am going count how many numbers I have after the decimal place.
00:06:31.800 --> 00:06:38.200
It has to be after the decimal place; 7, I only have one number.
00:06:38.200 --> 00:06:45.100
Take that number; place it over a 10.
00:06:45.100 --> 00:06:49.500
One 0 because I have only one number after the decimal place.
00:06:49.500 --> 00:06:54.100
So I am only going to have one 0 here.
00:06:54.100 --> 00:06:57.300
Let's go over more examples.
00:06:57.300 --> 00:07:01.100
Convert from fraction to decimal or decimal to fraction.
00:07:01.100 --> 00:07:09.200
Here we have a decimal; I am going to convert it to a fraction.
00:07:09.200 --> 00:07:18.100
If I look at this, if I have 25 cents, I have 1 quarter.
00:07:18.100 --> 00:07:26.400
1 quarter would be having 1 quarter out of... how many quarters equal a dollar?
00:07:26.400 --> 00:07:37.300
4; so having 1 quarter, 25 cents or 0.25, is the same thing as 1/4.
00:07:37.300 --> 00:07:45.300
Another way to do this, I take this number, 25.
00:07:45.300 --> 00:07:48.500
I am going to make that into my numerator.
00:07:48.500 --> 00:07:55.200
Then I am going to count how many numbers do I have after the decimal place?
00:07:55.200 --> 00:07:59.100
I have two numbers; I have one, two.
00:07:59.100 --> 00:08:07.200
I am going to put that many 0s after my 1 as my denominator.
00:08:07.200 --> 00:08:10.800
This becomes 25/100.
00:08:10.800 --> 00:08:19.500
I have to simplify this because this fraction... I know that 25 can go into 100.
00:08:19.500 --> 00:08:23.400
I am going to take this 25; I am going to divide by 25.
00:08:23.400 --> 00:08:29.200
Then I have to divide the bottom number by the same number.
00:08:29.200 --> 00:08:38.500
25 divided by 25 is 1; 100 divided by 25 is 4.
00:08:38.500 --> 00:08:46.800
0.25 is going to be the same thing as 1/4.
00:08:46.800 --> 00:08:56.100
The next example is a fraction 3/10; I can convert this into a decimal.
00:08:56.100 --> 00:08:58.500
Again let's relate it to money.
00:08:58.500 --> 00:09:05.700
If I have 10 as my denominator, then what do I have?
00:09:05.700 --> 00:09:12.900
10 parts to make a dollar would be 10 dimes.
00:09:12.900 --> 00:09:16.100
I know that I am working with dimes here.
00:09:16.100 --> 00:09:21.200
If I have 3 dimes, then how much do I have?
00:09:21.200 --> 00:09:29.400
How can I write that into a decimal?--I would have 30 cents.
00:09:29.400 --> 00:09:35.900
Having 3 dimes is the same thing as 30 cents.
00:09:35.900 --> 00:09:45.500
Or 3/10 is the same thing as 0.30 or 0.3 because again this is the same thing.
00:09:45.500 --> 00:09:52.200
I can put a 0 here because it is after the decimal place.
00:09:52.200 --> 00:10:01.300
Another way you can do this, just divide; 3 divided by 10.
00:10:01.300 --> 00:10:05.600
I have to add 0s at the end of it.
00:10:05.600 --> 00:10:11.800
10 goes into 30 three times; but I have to write it over the 0.
00:10:11.800 --> 00:10:16.800
Then I have to bring up my decimal; this becomes 30.
00:10:16.800 --> 00:10:21.400
If I subtract, I get 0.
00:10:21.400 --> 00:10:30.100
3/10 or 3 divided by 10 is going to be 0.3.
00:10:30.100 --> 00:10:37.400
This next example, 0.77, I am going to convert this into a fraction.
00:10:37.400 --> 00:10:52.900
If I have 0.77 or 77 cents, I have the same thing as 77 pennies.
00:10:52.900 --> 00:10:58.700
Again I can write that number at the top.
00:10:58.700 --> 00:11:02.300
How many pennies are equal to a dollar?
00:11:02.300 --> 00:11:05.400
I know that 100 are equal to a dollar.
00:11:05.400 --> 00:11:10.900
This is the same thing as saying I have 77 pennies.
00:11:10.900 --> 00:11:17.100
0.77 is the same thing as 77/100.
00:11:17.100 --> 00:11:25.600
Again without thinking of money, I can just take this number, 77, as my numerator.
00:11:25.600 --> 00:11:30.300
Count how many numbers I have after my decimal place which is 2.
00:11:30.300 --> 00:11:37.000
That means I am going to add two 0s which is 100 as my denominator.
00:11:37.000 --> 00:11:44.200
It is the same thing.
00:11:44.200 --> 00:11:51.900
This fourth example here, I have a fraction and I am going to convert this into a decimal.
00:11:51.900 --> 00:11:55.900
This top number tells me how many I have.
00:11:55.900 --> 00:12:01.700
This bottom number tells me how many out of 100 I have or how many out of a dollar I have.
00:12:01.700 --> 00:12:06.700
If I have 100 parts to make a dollar, what do I have?
00:12:06.700 --> 00:12:12.200
I have the penny because 100 pennies equals 1 dollar.
00:12:12.200 --> 00:12:14.200
I know that I have 9 of them.
00:12:14.200 --> 00:12:23.300
9 out of 100 would be the same thing as having 9 pennies.
00:12:23.300 --> 00:12:28.000
In order to write this as a decimal, if I have 9 pennies, how much do I have?
00:12:28.000 --> 00:12:33.600
I have 9 cents which is written like that.
00:12:33.600 --> 00:12:41.500
9 out of 100 is the same thing as 0.09.
00:12:41.500 --> 00:12:48.600
You can also think of this as 9 divided by 100.
00:12:48.600 --> 00:12:51.500
You can take 9 divided by 100.
00:12:51.500 --> 00:12:59.000
But since this is 100, I can do a shortcut here.
00:12:59.000 --> 00:13:07.100
Whenever my denominator is 10 or 100 or 1000, any number that is a multiple of 10,
00:13:07.100 --> 00:13:14.200
all I am going to do is take that top number... let's write that out; the top number is 9.
00:13:14.200 --> 00:13:16.000
I am going to count how many 0s I have here.
00:13:16.000 --> 00:13:20.000
I have one; I have two 0s.
00:13:20.000 --> 00:13:25.700
Since I have two 0s, I am going to take that number 2.
00:13:25.700 --> 00:13:32.100
I am going to place this decimal point right there.
00:13:32.100 --> 00:13:35.100
The decimal point always goes after the number.
00:13:35.100 --> 00:13:41.900
I am going to move the decimal point two places because again there are two 0s here.
00:13:41.900 --> 00:13:46.500
If I had a 10, I only have one 0.
00:13:46.500 --> 00:13:48.300
I would only move it one place value.
00:13:48.300 --> 00:13:53.300
If I had 1000, I would have three 0s.
00:13:53.300 --> 00:13:57.300
I would have to move it three place values.
00:13:57.300 --> 00:13:59.000
Again I am going to take this decimal point.
00:13:59.000 --> 00:14:04.400
I am going to move it two place values going to the left.
00:14:04.400 --> 00:14:08.100
I am going to go one and two.
00:14:08.100 --> 00:14:12.300
There is where my decimal point is going to go.
00:14:12.300 --> 00:14:15.800
Then I have a space right here; I have to put a 0 right there.
00:14:15.800 --> 00:14:21.200
For this shortcut, you can only do that if the denominator is a multiple of 10.
00:14:21.200 --> 00:14:26.400
It has to be 10, 100, or 1000, and so on.
00:14:26.400 --> 00:14:30.300
Otherwise you are going to have to do 9 divided by 100.
00:14:30.300 --> 00:14:32.600
Again this sign right here means divide.
00:14:32.600 --> 00:14:38.500
We can do 9 divided by 100 to change that into a decimal.
00:14:38.500 --> 00:14:47.800
But I also knew that this bottom number right here, it takes 100 pennies to make a dollar.
00:14:47.800 --> 00:14:52.300
Since it takes 100 pennies to make a dollar and I have 9 of them,
00:14:52.300 --> 00:14:58.100
I would have 9 cents; I can just write that as 0.09.
00:14:58.100 --> 00:15:01.000
That is it for this lesson; thank you for watching Educator.com.