Math Antics - Convert any Fraction to a Decimal - Free Educational videos for Students in K-12

Math Antics - Convert any Fraction to a Decimal - By mathantics

Transcript


00:0-1	Oh mm . In the last section we learned how
00:10	to convert some special-based 10 fractions into decimals and vice
00:14	versa . Now we're going to learn how to convert
00:16	any fraction into a decimal and it turns out to
00:19	be really simple . All you have to do is
00:21	divide sense of fraction is really just a division problem
00:25	. If you go ahead and do the division you'll
00:27	get an answer and that answer will be the decimal
00:29	value of the fraction . Now there's two ways we
00:32	can do the division , the easy way and the
00:34	hard way . Now , just because I mean we're
00:37	gonna start with the hard way , let's take the
00:40	fraction one half and converted into a regular division problem
00:43	with this division symbol . Now all we have to
00:45	do is follow the procedure for division , we just
00:48	see how many times this to divides into this one
00:52	. Oh it won't divide anytime , who is bigger
00:55	than one ? Looks like we're gonna need some help
00:58	and that's where the decimal point comes in . Now
01:01	. You remember that in the last section we learned
01:03	that one could be written as 1.0 or 1.00 or
01:07	1.000 and its value is still one . Let's try
01:11	doing that here and see what happens after the one
01:13	put a decimal point and then a zero in the
01:15	10th place . Now our division problem looks like 10
01:18	divided by two and that's easy to do . The
01:21	only difference is we have a decimal point . Let's
01:24	ignore the decimal point for a minute and pretend that
01:26	our problem really is 10 divided by two . So
01:29	too will go into 105 times because five times two
01:33	equals 10 and that leaves no remainder . So we're
01:35	done right ? Not so fast . We've got that
01:38	decimal point to deal with and we know that five
01:41	can't be the answer because five is bigger than one
01:43	half . We just need to include the decimal point
01:46	in our answer for it to be correct . We
01:48	put it directly above the decimal point in our problem
01:51	there . Now our answer is .5 or 0.5 which
01:54	is the more proper way to write it . So
01:57	by dividing we figured out that the decimal value of
01:59	1/2 is 0.5 . Now let's try converting the fraction
02:03	3/4 by dividing of course we start by rewriting our
02:07	fraction like this , three divided by four and again
02:10	we run into the same problem or it's too big
02:13	to go into three . So it looks like we're
02:14	gonna need a decimal point here too . Let's put
02:17	a decimal point after the three and a zero in
02:19	the 10th place to make 3.0 . Now our problem
02:23	almost looks like 30 divided by four . Now if
02:25	you remember your multiplication table , you'll know that four
02:28	goes into 37 times because seven times four is 28
02:33	. 30 -28 leaves a remainder of two but we
02:36	don't want a remainder . So let's keep going .
02:38	Four is too big to divide into two . So
02:41	the only way we can get rid of the remainder
02:43	is to use another zero in the hundreds place ,
02:45	which makes the number we're dividing up kind of look
02:47	like 300 . Now we can bring down that extra
02:50	zero to make the remainder look like 20 and four
02:53	will go into 25 times because five times four equals
02:56	20 and that leaves no remainder . Oh yeah ,
03:00	but don't forget we need to include the decimal point
03:02	in our answer . Now if you've kept your columns
03:04	lined up like I have , you'll see that the
03:06	decimal point goes right here and that makes our answer
03:09	0.75 . So the decimal value of 3/4 is 0.7
03:15	. All right . Let's convert one more of the
03:17	hard way . Let's find the decimal value of 1/3
03:20	by dividing 1x3 . Again , three is too big
03:23	to divide antoine . So we'll need to use a
03:25	decimal point and another zero which makes our problem look
03:28	like 10 divided by three . That's easy . Three
03:31	goes into 10 3 times because three times three equals
03:35	nine and that leaves a remainder of one just like
03:38	before we don't want to remainder . So let's use
03:40	another zero so we can keep on dividing . And
03:43	that gives us 10 divided by three again . Well
03:46	, we know that three goes into 10 3 times
03:48	and leaves a remainder of one . Uh huh .
03:51	Still the remainder of one . It looks like we're
03:53	gonna need another zero but that's just going to give
03:56	us 10 divided by three again which is going to
03:58	give us another remainder of one . This looks like
04:01	it might keep on going forever . Some fractions are
04:04	like that . If you divide them you'll see a
04:06	repeating pattern of numbers that continues on forever . So
04:10	the decimal value of one third is 0.333333333 and three
04:15	that keep on going forever . But since we can't
04:18	keep writing three's forever , we can just stop and
04:21	round the number off or we can use this special
04:23	symbol that means this number repeats forever . All right
04:27	, so all we have to do to convert a
04:29	fraction into a decimal is divide and so far we've
04:32	been doing that the hard way but now we're going
04:34	to do it the easy way . We're going to
04:36	use a calculator . Let's try a couple with a
04:39	calculator and see what we get to convert 1/4 .
04:42	We just punch in one divided by four and we
04:45	get 0.25 to convert two thirds . We just punch
04:49	in two divided by three and we get zero point
04:52	the whole lot of sixes looks like we have another
04:54	one of those repeating decimals , yep this way certainly
04:58	easier and quicker to but it's important to know how
05:01	to do it both ways . The five fractions that
05:04	we've just converted are so common that it's a good
05:06	idea to memorize their decimal values . Here they are
05:09	again , so you can review them 1/4 equal 0.251
05:14	3rd equals 0.333331 half equals 0.52 3rd equals 0.66666 and
05:22	3/4 equals 0.75 So that's how you convert any fraction
05:27	into a decimal . You just divide and we already
05:30	learned how to go the other way to convert a
05:32	decimal into a fraction in the last section . So
05:34	be sure to review it . If you need to
05:36	in the next section we're going to learn a few
05:39	tricks that we can use to help us compare the
05:40	values of fractions . But before that a quick review
05:44	to convert any fraction to a decimal number , all
05:47	you have to do is divide the top number by
05:49	the bottom . Usually when you divide a fraction you'll
05:53	need to do decimal division by using the decimal point
05:57	. You can keep writing zeros in the decimal number
05:59	of places and continue dividing until you have no remainder
06:03	. Sometimes decimal division results in a pattern that keeps
06:06	repeating forever . When that happens you can draw a
06:09	line over the repeating digits instead of writing them forever
06:12	once you know how to do decimal division . I
06:15	recommend that you convert fractions using a calculator since it's
06:18	quicker and easier . And as always be sure to
06:22	do the exercises and don't forget to practice dividing the
06:25	hard way too because if you're ever stranded on a
06:28	deserted island without a calculator , you need to be
06:30	able to do your at home . Mhm . To
06:35	see more free math videos , visit us online at
06:38	www dot math antics dot com .

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