Learn to Convert Decimals to Fractions (Change a Decimal into a Fraction) - [21] - Free Educational videos for Students in K-12

Learn to Convert Decimals to Fractions (Change a Decimal into a Fraction) - [21] - By Math and Science

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00:0-1	Hello . Welcome back . The title here is called
00:02	changing decimals to fractions . This is part one .
00:05	Another title might be converting decimals to fractions . This
00:09	is part one . In the last lesson we learned
00:11	how to go the other way . The last lesson
00:13	we started out with a fraction and we converted it
00:15	to a decimal because decimals and fractions are just different
00:19	ways of writing really the same information . So last
00:21	lesson we started with a fraction and we converted it
00:23	to a decimal equivalent here . We're going the other
00:26	way we're going to start with a decimal and then
00:28	we're going to convert it to a fraction equivalent .
00:30	Actually , these lessons are a little easier in my
00:32	opinion to do , they're a little easier to to
00:34	just actually do the work . So let's see how
00:36	to handle it . Let's say that I want to
00:39	take the decimal 0.3 and I want to convert it
00:43	to a fraction In a fraction . In simplest form
00:46	or in lowest terms . So what does this mean
00:48	by the way , the zero means zero holes .
00:50	I don't have any whole pizzas or any whole candy
00:53	bars . I have some fraction and the .3 represents
00:56	some fractional part . Uh when we get to .4.5.6.8.9
01:02	, then we roll over to get one whole candy
01:04	bar or one whole pizza . So we're really far
01:07	away from that . We only have a small fraction
01:08	of a pizza right now . What is the fraction
01:11	? Well , all you have to do is look
01:12	and say , well this is in the 10th place
01:14	because remember it goes tens , hundreds thousands , 10
01:18	thousands and so on . So to write this as
01:22	a fraction , all you have to do is recognize
01:24	that this is the 10th place . How many of
01:26	them do I have ? I have three of them
01:28	in the 10th place . It's 3/10 . That's actually
01:32	what this means . And since this fraction is already
01:35	simplified , I cannot divide top and bottom to simplify
01:38	it further . This is the final answer . So
01:40	you see this is a really important example for you
01:42	to really suck in and internalize it and just think
01:45	about it . This decimal is telling you everything you
01:48	need to know about the fractional thing , what it
01:50	means as a fraction . It's in the 10th place
01:52	. How many do I have ? Three of them
01:54	? So it's 3/10 . Remember we can count by
01:56	tents , 1/10 then 2/10 then 3/10 means I have
02:01	three little wedges of a pizza E each shaped to
02:04	be a size of 1/10 . I have three of
02:06	them . That's what this actually means . So to
02:08	write it as a fraction , it's 3/10 . If
02:10	I were to start with this and convert it to
02:13	a decimal , what would I do just from the
02:15	last lesson ? If I said , hey turn this
02:17	thing into a decimal , you would say okay ,
02:19	I'm gonna have an invisible decimal here , I'm dividing
02:21	by 10 because that's what it is . Is division
02:23	, I'm gonna move the decimal one spot to the
02:25	left , 0.3 , that's exactly it . So you
02:28	can go either way back and forth and get to
02:31	the same answers . It should all work out if
02:33	you're doing it all correct , it should all make
02:36	sense and give you all the correct answers no matter
02:37	which way you go . All right , let's take
02:41	a look at problem number two . If I can
02:43	ever get there problem number two , let's convert the
02:48	decimal 0.1 into a fraction . Well again this is
02:51	in the 10th place . So what does it mean
02:54	to have ? 0.1 ? I have one slice Worth
02:58	a 10th . So I have 1/10 . The one
03:01	goes up here and it's in the tense place .
03:03	The three goes up there and it's in the 10th
03:05	place . I cannot simplify this anymore . So the
03:07	answer is 1/10 . Now if I gave you instead
03:10	this and said go backwards , convert this to a
03:12	decimal , you would divide it , the decimal is
03:14	here invisible and you would move it by dividing by
03:17	10 0.1 . That's what we started with . So
03:21	that's what you have . All right , let's take
03:24	a look at problem number 30.4 . Let's convert that
03:28	to a fraction . Alright , so same story ,
03:31	it's in the 10th place . How many do I
03:34	have ? Four of them In the tense place ?
03:36	I have 4/10 . 4/10 . That's what that means
03:39	. But this fraction is not fully simplify . They're
03:42	both even numbers . I can take the four ,
03:45	I can take the 10 and I can simplify this
03:48	by dividing by two and dividing by 24 divided by
03:51	two is two . 10 , divided by two is
03:54	5 . This fraction I cannot simplify any further .
03:57	So this is the simplest fraction . That is 0.4
04:01	. If you go to a calculator and divide two
04:03	divided by five , this is what you're going to
04:05	get . If you take four and divided by 10
04:08	, you're going to get the same thing . This
04:09	fraction is equal 2.4 . This fraction is equal 2.4
04:13	. How can that be ? It's because these two
04:15	fractions are the same thing . I've just simplified it
04:17	to something simpler . So when we represent these as
04:21	a fraction , we always want the simplest form .
04:25	Let's take a look at the next problem . Let's
04:27	convert something a little more complicated . 1.2 . Let's
04:31	turn that into a mixed number . 1.2 . What
04:33	does this mean ? It means I have one whole
04:36	plus 10.2 which is a fractional part . So let's
04:39	ignore the whole for now only let's look at the
04:41	0.2 , The 0.2 . So let's look at this
04:46	. The 0.2 Is what ? 2/10 . Right ?
04:50	So this is in the tense place and there's two
04:53	of them , so too tense right now , can
04:55	I simplify this any further ? Well , two on
04:59	the top 10 on the bottom , I can divide
05:01	both . Top and bottom by two . So two
05:05	divided by two is one and 10 divided by two
05:07	is five . So what we figured out is that
05:10	the point to part of the problem is equal to
05:13	the fraction . 1/5 . So that's the fractional part
05:16	. But the original problem had one whole plus 1/5
05:20	. 1 whole plus 1/5 . How do you write
05:22	that together ? We say that it's one and 1/5
05:25	. So this would be the best way to write
05:27	it . One . Uh In 1/5 were converting it
05:30	into a mixed number . You could write this as
05:32	an improper fraction if you want . There's nothing wrong
05:34	with that . But when you have one whole plus
05:36	a fractional part is very common to write it like
05:38	this . If you wanted to make it into a
05:40	improper you would multiply one times five is five plus
05:43	one is 10 . Uh I'm sorry one plus five
05:46	is five plus one is not 10 plus one is
05:48	six . It would be 6/5 for the answer there
05:52	, but we'll just leave it in mixed number four
05:55	. All right , Halfway done . Let's take a
05:58	look at 0.002 . That is a decimal . We're
06:01	going to convert it to a fraction . All right
06:03	. So what do we do with this ? Well
06:05	, this is the 10th place . This is the
06:07	hundreds place . This is the thousands place . So
06:10	what is the value of this ? I have to
06:13	in the thousands place . I have two thousands right
06:17	? Not to tense because that would be here .
06:19	Not to hundreds because that would be here . But
06:21	two thousands . Which would be there to over 1000
06:25	. How do I simplify this fraction ? Well ,
06:28	I can divide top and bottom by two . They're
06:31	both even numbers two divided by two is one .
06:34	And what is 1000 divided by 2 . 500 .
06:39	So this is the simplest fraction that equals 0.0021 over
06:44	500 . Alright , next problem , Let's convert the
06:50	decimal 2.16 into a mixed number . So we're going
06:54	to ignore the two , we're only going to focus
06:56	on the 0.16 . This is what does this mean
07:00	? This is the 10th place and this is the
07:02	hundreds place . So I do have one in the
07:05	10th and six in the hundreds . But as a
07:08	whole together I have 16 in the farthest position over
07:13	here , which is the hundreds place . So you
07:15	write it as 1600s . I want to make sure
07:19	you understand that because you do have one in the
07:21	10th place and you do have six in the hundreds
07:25	place . But when you add all those together it's
07:27	the same as 16 in the hundreds place . This
07:29	is the same thing with regular numbers by the way
07:32	, let's go over here , The # 34 .
07:35	What does this mean ? It means I have I
07:38	have three in the 10th place and not the 10th
07:42	place . The tens place three tens and I have
07:45	four in the ones place . But all together we
07:48	put it together and we say it's 34 ones in
07:51	the farthest position . 34 1 . What about 76
07:54	? Yes , it's seven in the tens position .
07:57	For 70 work . This is worth 70 and this
08:00	is worth six in the one's position . So this
08:02	is worth something in the tens and this is worth
08:04	something in the ones . But we put them together
08:07	, we say that it's 76 ones . And so
08:10	here's the same thing , This is one in the
08:12	10th place , this is six in the hundreds place
08:15	. But all together it's 16 in the farthest position
08:18	in the hundreds position . So how do I simplify
08:21	this ? 16 1 hundreds ? What do I do
08:26	? Well , I know that I can divide the
08:28	top by four and the bottom by four because four
08:32	times four is 16 . So I divide and get
08:33	a 400 divided by four is 25 . And I
08:37	can't really simplify that any further . So I take
08:40	this fractional representation that was just talking about the .16
08:45	And then I attach it to the two holes for
08:47	two and four 25th as a mixed number . Two
08:51	and four 25th . If you wanted to write it
08:54	as an improper fraction , you could of course convert
08:55	that if you'd like . Alright , we're on the
09:01	home stretch . Just a few more problems . Let's
09:03	take a look at the number 1.01 . And we're
09:06	gonna convert that into a mixed number . So again
09:09	forget about the whole number . Let's just focus on
09:11	the .01 . So I have nothing in the 10th
09:15	place but only one in the hundreds place . So
09:18	I have 1 100 . All right . That's the
09:21	fraction . I can't simplify it anymore . I can't
09:24	divide top and bottom . So this is it .
09:25	And I attach it to the one so it's one
09:28	and 1 1/100 1 and 1 100 . That's the
09:32	final answer . Yeah . All right . Only three
09:36	more . Let's take a look at 8.6 and we're
09:39	gonna convert this into a mixed number . Same thing
09:42	. We're gonna ignore the whole number . We're gonna
09:44	focus only on the 0.6 And this is in the
09:47	10th place . So what does this mean ? Six
09:49	in the 10th place ? Now I can simplify this
09:53	by dividing top and bottom by what ? By two
09:56	? They're both even numbers . And what will I
09:59	get ? Six divided by two is three and 10
10:02	divided by two is five . So 3/5 is what
10:04	the 50.6 means . I attach it to the whole
10:07	of eight , eight and 3/5 . This means eight
10:11	plus 3/5 . This means one plus 1 , and
10:14	so on and so forth . All right . Only
10:19	two more problems than we're done . Let's take a
10:22	look at 2.4 to convert this to a mixed number
10:27	. Let's focus on the 0.42 So yes , I
10:31	do have four in the tents and I have to
10:33	in the hundreds . But again , taken as a
10:35	whole , I have 42 in the farthest position ,
10:38	which is the hundreds place . 42 hundred's . That's
10:41	what I have tens , hundreds . 42 hundred's .
10:44	How do I simplify this ? I can say 42
10:48	. 100 And I can divide top and bottom by
10:52	two . Yeah . Now if you take 42 and
10:57	you go and do the long division , divide by
10:58	two you're going to get 21 and 100 divided by
11:02	two is 50 . So this fraction 21 50th is
11:05	what ? 2.42 means I'm sorry 0.42 means now we
11:09	attach it to the two and 21 50th . So
11:13	this is the representation of this decimal form 2.42 two
11:20	and 21 50th And then we have the final question
11:24	which is 3.5 , Convert that to a mixed number
11:28	. Let's work on the 0.5 . This means I
11:31	have in the 10th place . I have five of
11:33	them five in the 10th place . 5/10 . Now
11:38	I want to simplify this . What do I do
11:39	? Well 5/10 . I can divide the top by
11:42	five and I can divide the bottom by five .
11:45	So five divided by five is one and 10 divided
11:48	by five is too . So I get one half
11:50	and then I attach it to the whole number which
11:52	is the three making it three and one half .
11:57	So again I hope you can see that fractions and
11:59	decimals really do . They really are joined at the
12:01	hip and you can see it right here . When
12:03	we talk about decimals , the place values are fractional
12:07	. Their tents there , hundreds , there are thousands
12:10	. That's why fractions and decimals go together because they
12:13	are really just they're tied together in our representation of
12:16	what numbers are in what decimals really are . All
12:19	of the decimal values are fractions tens , hundreds thousands
12:24	, 10 thousands 100 thousands millions . As you keep
12:28	going down and down in the decimals . I'd like
12:30	you to solve every one of these yourself . Follow
12:32	me on the part . Two will wrap up your
12:33	practice with converting a decimal into a fraction

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