Convert Any Decimal to a Fractions - easy math lesson - Free Educational videos for Students in K-12

Convert Any Decimal to a Fractions - easy math lesson - By tecmath

Transcript


00:00	Welcome to the Tech Math channel . What we're gonna
00:02	be having a look at in this video is going
00:04	to be looking at converting between decimals into fractions .
00:07	Okay , so with this we're gonna be looking uh
00:10	there's a couple of tricks with this and we're gonna
00:12	be looking at some uh decimals , but you're a
00:15	little bit more difficult than others . So we're gonna
00:16	start out with the easy ones . These are ones
00:19	which are terminated one , things like 10.5 or say
00:23	.75 where they don't just keep going on and on
00:25	, they only maybe go to 1234 desperate places .
00:28	And then they stopped . The other ones are gonna
00:31	be looking at a recurring decimals and these ones say
00:34	like point One recurring here . That is like 0.111111
00:41	where it just keeps going on and on and on
00:43	and on and on . And we're gonna look at
00:44	how to change these also into fractions . So we'll
00:47	look at these uh well look at these after these
00:50	particular ones here . So let's do these ones first
00:53	. So so we had to say something like this
00:55	, you might already think , hey , I know
00:56	that this actually is as a fraction and that's probably
00:59	a good thing if you do . But I'll show
01:01	you how you go about converting these first off ,
01:05	the easiest way doing these Is pretty much you get
01:09	75 here . And these are , these are actually
01:12	finally not known as decimals but they're also known as
01:14	decimal fractions . And what this means is they are
01:18	fractions of basically the next Number up divisible by zero
01:23	. Give an example here's 75 . The next number
01:25	up a that's a zero number is 100 . So
01:29	this is 75 out of 100 . Okay . And
01:32	then we can go through and see what number goes
01:35	into both the top and the bottom . So number
01:37	that goes into both , the top of the bottom
01:38	here is 25 , 25 goes into 75 three times
01:44	. And it goes into the bottom number 100 four
01:47	times . So .75 Is the same as 3/4 .
01:52	So they're fairly easy . These ones , I'll give
01:54	you one more example of these . I'll give you
01:57	a hard for example , One that you might not
01:58	know off the top of your head . Uh say
02:01	we had to change this one here , 0.18 75
02:07	. And we wanted to change this into a fraction
02:11	. Okay , so again this is a decimal fraction
02:14	that we actually have here . And we can actually
02:17	, if we really wanted to be really , really
02:20	save a lot of time and effort , I guess
02:22	we could sit there and say , well this is
02:24	a fraction , is that ? This is a fraction
02:30	. What is needed is 1,875 by the next zero
02:35	number of which is 10,000 Okay , it's okay .
02:40	That's that's a fraction that we can leave it there
02:41	. But let's simplify this . So we could We
02:44	can look at a number that goes into both of
02:46	these . I think the number which you might recognize
02:48	, it goes into both because this is a 75
02:50	year would be 25 , 25 . If you do
02:54	a quick conversion here , a quick division . This
02:57	goes into 1875 , 25 goes in 75 times and
03:05	into 10,000 he goes 400 times . Then we can
03:10	convert this further . We can we can simplify this
03:12	further because 25 also goes into both of these numbers
03:16	to goes into 75 three times when I do this
03:19	, difficult three times And it goes into 416 times
03:24	. Yeah , we can't get simplify this any further
03:27	. So this is our answer . 3/16 . Okay
03:30	, so there we go . That's how we go
03:34	about converting Just these terminating type decimals and they're they're
03:39	fairly easy , but let's get into the next one
03:41	. These are also actually quite easy . It's just
03:43	knowing the trick on how to do them . So
03:44	let's have a look at how you go about converting
03:47	recurring decimals now , what about I'll give you an
03:50	example here . So we wanted to change this one
03:53	here . 0.7 that if it had a dot there
03:57	And so it would keep going on and on .
03:59	777777 . Okay , and so on and so forth
04:05	. So let's change this , I'll show you how
04:07	to change this into a fraction now . First off
04:12	it's just a couple of little algebraic things here ,
04:14	which are kind of handy . They're not really heavy
04:16	call heavy duty older group . But first off ,
04:19	let's get this 0.777777 , we're gonna get that to
04:24	equal x . Okay . Yeah , there's a little
04:29	trick we do here . Now if we have a
04:31	look here , we basically want to get a decimal
04:33	place between , this is the first part of the
04:35	trickier . We want to get a decimal place between
04:38	um These two particular armed recurring numbers here . So
04:42	the way we can do this is that we multiply
04:44	both sides by 10 because this would become 7.77 dot
04:50	on and on and on and on and on and
04:52	on and this would equal 10 X . Pretty good
04:55	. Do you see that ? Okay , so we're
04:57	going to call this one up here equation one and
05:00	this one here equation too , you're still with me
05:05	. I hope so . So what we're gonna do
05:06	now this is the master trick is we're going to
05:09	subtract equation one from equation too . And if we
05:13	do this we get this as follows 10 X .
05:17	Takeaway eggs is nine X . And 7.7777 . So
05:22	and so and so and so and take away .77777
05:28	. Okay . Do you see how that worked ?
05:31	That's pretty cool . Right . Because what you might
05:33	realize now is we can do it we can basically
05:35	divide but we can get X by itself by dividing
05:38	both sides by nine . And if we do this
05:40	, what we get is as follows we basically get
05:44	Xia on this side by itself Because we divided nine
05:49	and got rid of the nine here and we've got
05:51	this seven here and we've divided by nine . And
05:55	we have changed it into a fraction right ? Actually
05:58	it was seven over 979 . It's not bad .
06:02	It's it's actually not too bad . So what about
06:04	I'll give you another example of these . All right
06:12	now to say we do one , what about we
06:15	have 0.24 , two , So so so did it
06:23	and that goes on and on and on . So
06:26	you're gonna see here we're gonna end up getting the
06:27	decimal place between these guys the first part of our
06:30	recurring numbers here . Okay , so let's make this
06:33	again legal . X . And this time to get
06:39	but the decimal place between are occurring numbers here .
06:42	We're gonna be after 24 . Would 2 4-4 did
06:49	it a little bit . And to do that we
06:52	have to multiply this expression here by not 10 this
06:55	time by 100 . Okay because the decimal place jobs
06:58	two times . So we end up with 100 eggs
07:04	. Okay , we'll call this one here , equation
07:07	one . We'll call this one here equation too .
07:11	So we'll take equation one away from equation too .
07:15	100 X . Takeaway X . is 99 x equals
07:23	. And equation this part this side here , this
07:26	one take away this one we're going to basically are
07:29	get this one all by itself . We're gonna get
07:31	this get rid of this 24 to 4 to 4
07:33	to 4 and we're gonna be stuck with the number
07:36	24 . Okay , So this is what we're up
07:43	to so far . We divide both sides now as
07:46	you see by 99 x . By itself , 99
07:50	. Extra water by 99 x . And this one
07:53	becomes 24 Over 90 . And that's our answer .
07:59	Okay . So how did you go with her ?
08:02	Pretty good ? Um Hopefully that was that was not
08:06	too bad for you . Um Anyway , I hope
08:10	you understood both of those methods , and we'll see
08:13	you next time . Okay , bye .

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