Math Antics - Converting Any Fraction - Free Educational videos for Students in K-12

Math Antics - Converting Any Fraction - By mathantics

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00:03	Uh huh . In the last section we learned how
00:07	to convert some special based in fractions into decimals and
00:11	vice versa . Now we're going to learn how to
00:13	convert any fraction into a decimal and it turns out
00:16	to be really simple . All you have to do
00:18	is divide sense of fraction is really just a division
00:21	problem . If you go ahead and do the division
00:23	you'll get an answer and that answer will be the
00:26	decimal value of the fraction . Now there's two ways
00:29	we can do the division . The easy way and
00:31	the hard way . Now , just because I mean
00:33	we're gonna start with the hard way . No let's
00:36	take the fraction one half and converted into a regular
00:39	division problem with this division symbol . Now all we
00:42	have to do is follow the procedure for division ,
00:44	we just see how many times this to divides into
00:47	this one . Oh it won't divide any time ,
00:51	who is bigger than one looks like we're gonna need
00:54	some help and that's where the decimal point comes in
00:58	. Now . You remember that in the last section
01:00	we learned that one could be written as 1.0 or
01:02	1.00 or 1.000 . And its value is still one
01:07	. Let's try doing that here and see what happens
01:10	after the one . Put a decimal point and then
01:12	a zero in the 10th place . Now our division
01:14	problem looks like 10 divided by two and that's easy
01:17	to do . The only difference is we have a
01:19	decimal point . Let's ignore the decimal point for a
01:22	minute and pretend that our problem really is 10 divided
01:25	by two . So too will go into 105 times
01:28	because five times two equals 10 and that leaves no
01:31	remainder . So we're done right ? Not so fast
01:35	. We've got that decimal point to deal with and
01:37	we know that five can't be the answer because five
01:39	is bigger than one half . We just need to
01:42	include the decimal point in our answer for it to
01:44	be correct . We put it directly above the decimal
01:46	point in our problem there . Now our answer is
01:49	.5 or 0.5 which is the more proper way to
01:52	write it . So by dividing we figured out that
01:55	the decimal value of 1/2 is 0.5 . Now let's
01:59	try converting the fraction 3/4 by dividing of course we
02:03	start by rewriting our fraction like this three divided by
02:06	four and again we run into the same problem or
02:09	is too big to go into three . So it
02:11	looks like we're gonna need a decimal point here to
02:14	let's put a decimal point after the three and a
02:16	zero in the 10th place to make 3.0 . Now
02:19	our problem almost looks like 30 divided by four .
02:22	Now if you remember your multiplication table you'll know that
02:25	four goes into 37 times because seven times four is
02:29	28 . 30 -28 leaves a remainder of two but
02:33	we don't want a remainder so let's keep going .
02:35	Four is too big to divide into two . So
02:38	the only way we can get rid of the remainder
02:40	is to use another zero in the hundreds place ,
02:42	which makes the number we're dividing up kind of look
02:44	like 300 . Now we can bring down that extra
02:47	zero to make the remainder look like 20 and four
02:50	will go into 25 times because five times four equals
02:53	20 and that leaves no remainder . Oh yeah but
02:57	don't forget we need to include the decimal point in
02:59	our answer . Now if you've kept your columns lined
03:01	up like I have , you'll see that the decimal
03:03	point goes right here and that makes our answer 0.75
03:08	. So the decimal value of 3/4 is 0.75 .
03:12	All right . Let's convert one more of the hard
03:14	way . Let's find the decimal value of 1/3 by
03:17	dividing 1x3 . Again . Three is too big to
03:20	divide antoine . So we'll need to use a decimal
03:23	point and another zero which makes our problem look like
03:25	10 divided by three . That's easy . Three goes
03:28	into 10 3 times because three times three equals nine
03:32	and that leaves a remainder of one just like before
03:35	we don't want to remainder . So let's use another
03:38	zero so we can keep on dividing . And that
03:40	gives us 10 divided by three again . Well ,
03:43	we know that three goes into 10 3 times and
03:46	leaves a remainder of one . Huh ? Still the
03:49	remainder of one . It looks like we're gonna need
03:51	another zero . But that's just going to give us
03:53	10 divided by three again . Which is going to
03:55	give us another remainder of one . This looks like
03:58	it might keep on going forever . Some fractions are
04:01	like that . If you divide them , you'll see
04:03	a repeating pattern of numbers that continues on forever .
04:06	So the decimal value of one third is 0.333333333 and
04:12	three that keep on going forever . But since we
04:15	can't keep writing three's forever , we can just stop
04:18	and round the number off or we can use this
04:20	special symbol that means this number repeats forever . All
04:24	right . So all we have to do to convert
04:26	a fraction into a decimal is divide and so far
04:29	we've been doing that the hard way but now we're
04:31	going to do it the easy way . We're going
04:33	to use a calculator . Let's try a couple with
04:36	a calculator and see what we get to convert 1/4
04:39	. We just punch in one divided by four and
04:42	we get 0.25 to convert two thirds . We just
04:46	punch in two divided by three and we get zero
04:48	point the whole lot of sixes looks like we have
04:51	another one of those repeating decimals , yep this way
04:55	certainly easier and quicker to but it's important to know
04:58	how to do it both ways . The five fractions
05:01	that we've just converted are so common that it's a
05:03	good idea to memorize their decimal values . Here they
05:06	are again , so you can review them . 1/4
05:09	equal 0.251 3rd equals 0.333331 half equals 0.52 3rd equals
05:17	0.66666 and 3/4 equals 0.75 So that's how you convert
05:24	any fraction into a decimal . You just divide and
05:27	we already learned how to go . The other way
05:28	to convert a decimal into a fraction in the last
05:30	section . So be sure to review it . If
05:32	you need to in the next section we're going to
05:35	learn a few tricks that we can use to help
05:37	us compare the values of fractions . But before that
05:40	, the quicker you to convert any fraction to a
05:43	decimal number , all you have to do is divide
05:45	the top number by the body number . Usually when
05:49	you divide a fraction you'll need to do decimal division
05:52	by using the decimal point . You can keep writing
05:55	zeros in the decimal number of places and continue dividing
05:58	until you have no remainder . Sometimes decimal division results
06:02	in a pattern that keeps repeating forever . When that
06:05	happens , you can draw a line over the repeating
06:07	digits instead of writing them forever once you know how
06:11	to do decimal division . I recommend that you convert
06:13	fractions using a calculator since it's quicker and easier .
06:17	And as always , be sure to do the exercises
06:20	and don't forget to practice dividing the hard way too
06:23	, because if you're ever stranded on a deserted island
06:26	without a calculator , you need to be able to
06:28	do your at home party , learn more at math
06:33	antics dot com .

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