Math Antics - Converting Base-10 Fractions - Free Educational videos for Students in K-12

Math Antics - Converting Base-10 Fractions - By mathantics

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00:03	Uh huh . Now that we know the basics of
00:07	how decimal numbers work , Let's see how we can
00:09	write some special fractions using decimal numbers . I'm going
00:13	to call these fractions based 10 fractions because they're bottom
00:16	numbers are all powers of 10 . Like 10 100
00:19	or 1000 . Let's start with this fraction 1/10 .
00:23	You should recognize that it's one of our building blocks
00:26	. And this should be easy to write down as
00:27	a decimal number because we have a number of place
00:30	just for counting 10th . So all we have to
00:33	do is put one in the 10th place like this
00:36	0.1 . Now when you write decimal numbers it's important
00:40	that you always include the ones place . But since
00:42	we don't have anyone's we just put a zero in
00:45	that spot . The zero makes the decimal point easier
00:47	to see . All right , so that's 1/10 .
00:50	But what if we have to over 10 instead ?
00:52	Well all we have to do is change the digit
00:54	in the 10th place to a two . So to
00:57	over 10 equals 0.2 . In fact we can keep
01:01	counting 10th like this . 3/10 456789 and finally 20th
01:07	. But look what happened when we got to 20th
01:10	now we don't have a digit for 10 . So
01:11	we had to use the next number place over the
01:13	ones place . But that makes sense because if you
01:16	have the fraction 10/10 that makes a whole and the
01:19	value is just one . Of course we don't really
01:21	need the zero in the 10th place to write one
01:24	but as long as the decimal points there at least
01:26	we won't confuse it with tin . Alright 10th are
01:29	pretty easy . But what about hundreds ? Let's start
01:31	with the hundreds . Building block one over 100 .
01:34	To write that as a decimal , we simply put
01:36	a one in the hundreds place . We also need
01:39	to put a zero in the 10th place to act
01:41	as a placeholder and show that we have no tents
01:43	and we still need to put a zero in the
01:45	ones place as usual . Next let's try to hundreds
01:49	for that . We simply put it to in the
01:50	hundreds place . Let's keep on counting with hundreds ,
01:53	just like we did for 10th 304 56789 and 10
01:59	hundreds . Ah but look what happened when we got
02:02	to 10 hundreds , just like before we have to
02:04	use the next number place to the left , the
02:06	10th place . This happens because any time you have
02:09	10 of a building block , they combined to form
02:12	one of the next biggest building block . For example
02:16	, 1000s is a 10th . 10/10 is a one
02:20	, 10 ones is a 10 and 10 tens is
02:23	100 . Now , the next fraction after 10 over
02:26	100 is 11 over 100 . Now , if you
02:28	think about it , you'll see that 11 hundreds is
02:30	really just a combination of 10 hundreds and 100 .
02:34	Knowing that will help us write it as a decimal
02:36	because a group of 10/100 is equal to 1/10 .
02:39	We put a one in the 10th place and we
02:41	still have that 1/100 leftover . So we put a
02:44	one in the hundreds place , they're 11 over 100
02:48	is just 0.11 as a decimal . Fortunately you don't
02:52	have to break up the fraction into 10th and 100th
02:54	each time anytime you have a two digit number over
02:57	100 all you have to do is put those digits
02:59	into the 10th and 100th . Place of your decimal
03:01	number . Let's look at a few more examples to
03:04	help you see the pattern . 24 over 100 would
03:07	be 0.24 32 over 100 would be 0.3 to 78
03:12	. Over 100 would be 0.78 and 99 over 100
03:16	would be 0.99 Now what do you think will happen
03:19	if we convert the fraction 100 over 100 into a
03:22	decimal ? Right 100 has three digits so we need
03:25	to use another number . Place Now . The next
03:27	one over is the ones place . And that makes
03:29	sense because 100 over 100 is a whole and its
03:32	value is just one . Now that we know how
03:35	to convert hundreds into decimals . Let's try converting thousands
03:38	. That's fractions that have 1000 as the bottom number
03:41	. Let's start with one over 1000 . Now this
03:44	should be easy . All we have to do is
03:45	put a one in the thousands place . Notice that
03:48	this time we need zeros in both the 10th and
03:50	100th place to act as placeholders . Next , Let's
03:53	strike in burning 10 over 1000 . Remember that 10,000
03:57	is the same as 100 . So put a one
03:59	in the hundreds place and we'll put a zero in
04:02	the thousands place . We don't really need the zero
04:04	at the end , but it helps us see that
04:06	this was 10 thousands . All right . What if
04:09	we have 100 over 1000 ? That's a three digit
04:11	number on top . So , we're going to need
04:13	to use three number places , the thousands place the
04:15	hundreds place on the 10th place . So , as
04:19	you can see , 100 over 1000 is just the
04:21	same as 1/10 . Let's see a few more examples
04:24	, 58 over 1000 is 0.58 73 Over 1000 is
04:29	0.73 365 . Over 1000 is 0.365 and 999 over
04:37	1000 is 0.999 . And finally , what do you
04:41	think we could get if we converted 1000 over 1000
04:44	? Right ? Again , 1000 over 1000 is just
04:46	a whole . So its value would be one .
04:48	Okay , so we've learned how to convert based in
04:51	fractions into decimals . But we can go the other
04:53	way to we can start with the decimal and convert
04:56	it into a fraction . Let's say we want to
04:58	convert a decimal number into a fraction . All we
05:01	have to do is take the decimal digits and make
05:03	them the top number of a based infraction . The
05:06	bottom number will be determined by the smallest number place
05:08	used in our decimal for example , to convert 0.8
05:12	into a fraction , we put an eight on the
05:14	top and a 10 on the bottom because the smallest
05:16	number place in our decimal was the 10th place .
05:19	And to convert 0.29 into a fraction we put a
05:22	29 on top and we put 100 on the bottom
05:25	because the smallest number place in our decimal was 1/100
05:28	place . And finally to convert 0.568 into a fraction
05:32	we put 568 on top and 1000 on the bottom
05:36	because the smallest number place on our decimal was the
05:38	thousands of place . Okay , so far all of
05:41	the fractions that we've converted to decimal numbers and vice
05:44	versa have bottom numbers like 10 , 100 or 1000
05:48	. Those fractions are easy to convert because our number
05:50	system is based on powers of 10 . We have
05:53	number of places specifically for counting those . But what
05:56	if we want to take fractions with different bottom numbers
05:58	like one half 3/4 or eight 25th and write those
06:02	as decimal numbers . We don't have special number of
06:04	places for halves , fourths or 25th . So what
06:07	are we going to do ? Well you're gonna have
06:09	to watch the next section to find out . But
06:11	first let's take a minute and review all this .
06:14	If a fraction has a bottom number that is a
06:16	power of 10 , then it's easy to convert it
06:19	into a decimal number because there are a number of
06:20	places just recounting based infractions To convert tents . All
06:25	you have to do is put the top number in
06:27	the 10s . pl to convert hundreds . You have
06:30	to use both attempts and the hundreds of place together
06:33	. To convert thousands , you have to use three
06:36	number of places and so on . You can also
06:40	convert from a decimal number two , a fraction .
06:42	Just by making the decimal digits , the top number
06:44	of the fraction , and by using a bottom number
06:46	that's based on the smallest number . Place from our
06:48	decimal . You sure to do the exercises So you
06:51	get really good at converting based infractions . Learn more
06:56	at math antics dot com .

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