Math Antics - Decimal Place Value - Free Educational videos for Students in K-12

Math Antics - Decimal Place Value - By Mathantics

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00:03	Uh huh . Hi , I'm rob . Welcome to
00:07	Math antics . In this video we're going to learn
00:09	about decimal place value . As that name suggests .
00:12	It's related to regular place value so be sure to
00:15	watch our video about that if you haven't already In
00:18	the previous video we learned how to count . Using
00:20	just 10 different digits and a number of places that
00:23	represent different sized groups . For example if we needed
00:26	account , 235 apples . We use different number of
00:30	places for accounting by ones by groups of 10 and
00:33	by groups of 100 . The digit two in the
00:35	hundreds place represents two hundred's . The three in the
00:39	tens place represents three tens or 30 and the five
00:42	in the ones place represents five ones or just five
00:46	. It's a pretty amazing system . If you think
00:48	about it , it only has 10 digits , but
00:50	those digits can be reused in different combinations to count
00:54	any number from zero all the way to trillions of
00:57	apples and beyond . But as amazing as it is
01:01	, there's just one little problem with our number system
01:03	so far . What if you don't have a whole
01:09	apple in the place value video . We only learned
01:13	how to count whole amounts or what we call whole
01:15	numbers which is the set of numbers you get if
01:17	you start with zero and then count by ones 1234
01:21	and so on . But there are things besides whole
01:25	amounts , it's possible to have just part of something
01:28	like just part of an apple . And that means
01:30	they're in between amounts . You might have one apple
01:33	or two apples but you could also have something in
01:36	between that like 1.5 apples . How can the base
01:39	10 number system handle situations like that ? The answer
01:42	is decimal places . Decimal places are a way of
01:46	extending the base 10 number system so that it can
01:49	represent amounts that are in between whole amounts , decimal
01:52	places are just like regular number places except that instead
01:55	of using them to count groups , we use them
01:58	to count parts or fractions of things To see how
02:01	the base 10 system is extended with decimal places .
02:04	Let's look at the pattern of number places that we
02:06	saw in the last video . We started out with
02:09	a number of place for counting things one at a
02:11	time . And when we hit the limit of counting
02:13	with it , we used another number place on the
02:15	left side of it for counting groups of 10 .
02:18	By combining those two number places , we could count
02:21	from zero all the way up to 99 . But
02:24	when we needed to count beyond that we used another
02:26	number place on the left side of it for counting
02:29	groups of 100 . And when those places were maxed
02:31	out , we added a place for counting by groups
02:33	of 1000 and then by groups of 10,000 and so
02:36	on . See the pattern . Each time we added
02:39	a new number place it was located to the left
02:42	of the previous one And each time it represented groups
02:45	that were 10 times larger than the previous group .
02:48	Since the amounts that a number of places represent get
02:51	bigger and bigger as we go to the left ,
02:53	it makes sense that number of places for counting smaller
02:56	amounts like parts of something that are less than one
02:58	will need to go on the right side of the
03:00	once place , that's where the decimal places are found
03:03	. And just like the whole number of places can
03:06	go on forever To the left counting bigger and bigger
03:08	groups , the decimal number places can go on forever
03:11	to the right counting smaller and smaller parts or fractions
03:16	but if number places go on forever in either direction
03:20	then how do we know which places which I mean
03:22	? If they all look the same or worse ,
03:24	if they're invisible then how do we know which digit
03:27	goes in which place ? Ah that's an excellent question
03:30	. We do have a problem . Now that number
03:32	of places can extend in both directions . Before when
03:36	we had only whole number of places that extended in
03:38	just one direction to the left , we knew that
03:41	the place that was furthest to the right was always
03:44	the ones place . But now we know that number
03:47	of places can extend in both directions . So we
03:49	need a new way to tell which places which what
03:52	we need is a point of reference , a place
03:55	that we always start from . And for that we
03:58	use a special symbol called the decimal point , which
04:01	in the United States looks just like a period .
04:04	Basically the decimal point acts as a separator . It
04:07	separates the number of places that are used for counting
04:09	whole values which are on the left side of the
04:11	decimal point from the number of places that are used
04:13	to count fractional values which are on the right side
04:16	of the decimal point . And that's why you don't
04:18	see a decimal point in every number . If there's
04:21	no decimal digits in a number like in the whole
04:23	number 25 then you don't need to show the decimal
04:26	point . It's safe to assume that the digit farthest
04:28	to the right is in the ones place . Of
04:31	course you could still show the decimal point if you
04:33	wanted to since it's always immediately to the right of
04:35	the ones place . But if there's no decimal digits
04:38	then we don't need to separate them from the whole
04:40	number digits . If a number does have decimal digits
04:44	then we call it a decimal number and the decimal
04:46	point helps us quickly recognize which digit is in the
04:49	ones place . For example if you see a sequence
04:52	of digits like this 1-6.53 you can tell right away
04:58	that the digit six is in the ones place because
05:00	it's immediately to the left of the decimal point .
05:03	That means this too is in the 10s place and
05:06	this one is in the hundreds place . Okay but
05:09	what about the digits that are to the right of
05:11	the decimal point ? We know that they must be
05:13	in decimal number of places . But what are the
05:16	names of those decimal number places ? And what values
05:18	do they count ? Well looking back at our number
05:21	place pattern , we see that each time we move
05:23	to the left the new number place counts amounts that
05:26	are 10 times bigger than the previous place . So
05:30	each time we move to the right , that place
05:32	should count amounts that are 10 times smaller than the
05:35	previous place . Since the ones place counts by ones
05:39	, the number place to the right of it should
05:41	count by amounts that are 10 times smaller than one
05:44	. The amount that's 10 times smaller than one is
05:46	called a 10th . It's the amount you get .
05:49	If you take one whole like one whole apple invited
05:52	into 10 equal parts , keeping just one of them
05:55	, 1/10 is what we call a fraction . And
05:58	fractions are written using a special notation that has two
06:01	numbers with the line between them . The number on
06:04	the bottom tells how many equal parts the whole amount
06:07	is divided into and the top number tells you how
06:10	many of those parts you have . So the fraction
06:12	1/10 is written like this , 1/10 . Getting back
06:17	to our apple counting example . Previously we could only
06:20	count whole apples but now that we have a number
06:23	of place for counting 10th , we can count 10th
06:25	of apples to we can use the once place and
06:28	the 10th place together to count amounts that are in
06:31	between a whole number of apples to see how it
06:34	works . Let's start our counting with one whole apple
06:37	and no 10th . That means that there will be
06:39	a one in the ones place and a zero in
06:41	the 10th place . But now let's start adding 10th
06:44	to that for each 10th that we count . We
06:47	increase the digit in the 10th place by one 1/10
06:51	. 2/10 3 10th 45 Let's pause for a second
06:55	to notice something important . Do you see that having
06:58	5/10 of an apple is the same as having one
07:00	half of an apple ? That's because five is exactly
07:04	half of 10 And the fraction 5/10 can be simplified
07:08	to 1/2 . That's why having 1.5 apples is the
07:12	same as having 1.5 apples . Pretty cool . Huh
07:15	? Anyway , back to counting 6/10 78 and 9/10
07:20	. Now we have one whole apple and also 9/10
07:23	of an apple . But our 10th place is maxed
07:26	out with the digit night that's as high as it
07:28	can count . So what do you think will happen
07:30	if we add one more 10th , Yep those 10/10
07:34	combined to form one whole apple . And that will
07:36	cause our once placed digit to increase to a two
07:39	, we now have two whole apples . Even though
07:42	one is made up from slices , the amount is
07:44	still equal to one hole . See how decimal digits
07:47	. Help us count in between whole amounts . But
07:49	wait there's more more decimal number of places that is
07:53	the 10th place allows us to count in between the
07:56	ones . But what if we want to count amounts
07:58	that are in between the 10th ? The decimal number
08:03	places keep on going to the right and each time
08:06	they count amounts that are 10 times smaller than the
08:08	previous amount . So if the 10th place counts fractions
08:12	that are 1/10 of one , then the next number
08:14	of place over will count amounts that are 1/10 of
08:17	1/10 . 1/10 is called 100th . And it's the
08:22	fraction you get if you take a 10th and then
08:24	divide it into 10 equal parts . It's a very
08:27	small fraction and it's called 100 because it's the same
08:31	fraction you'd get if you take a whole and divided
08:33	up into 100 parts . So it's fraction form looks
08:36	like this one over 100 . Just like 10th could
08:41	be used to represent amounts that are in between the
08:43	ones . Hundreds can be used to represent amounts that
08:47	are in between 10th and just like if you combine
08:50	20th , they equal one . If you combine 10
08:53	hundreds , the equal 1/10 And the decimal number places
08:57	keep on going like that . The next number place
09:00	over represents fractions that are 1/10 of 100 . That
09:04	very small fraction is called 1000 because it would take
09:07	1000 of them to make one whole . And the
09:09	next place over is 10 times smaller than that .
09:12	It's called the 10,000th place . And then there's 100,000
09:16	place , there's the millionth place and so on .
09:20	So do you see how truly amazing our number system
09:23	is ? It can represent any whole number amount no
09:25	matter how big by adding bigger and bigger number places
09:28	to the left , but it can also represent amounts
09:31	in between those whole amounts with more and more precision
09:34	down to the tiniest fraction imaginable by adding more and
09:37	more decimal number of places to the right . That
09:40	is truly amazing . In fact it kind of makes
09:43	my head hurt just thinking about it . Of course
09:46	it could be this dog on pot to wear my
09:48	head all the time . Okay , so now that
09:51	you know how decimal places work , let's talk briefly
09:53	about how we can show their place value and how
09:55	we can write decimal numbers and expanded form a digits
09:59	value is determined by the place that it's in .
10:02	So if a two is in the 10th place ,
10:03	it stands for 2/10 which can be written with the
10:06	fraction 2/10 . If a three is in the 10th
10:09	place that stands for 3/10 or 3/10 . If a
10:13	four is in the 10th place that stands for 4/10
10:16	or for over 10 and so on . And just
10:19	like A two in the 10th place stands for the
10:21	place value 2/10 . A two in the hundreds place
10:24	stands for the place value to hundreds and A two
10:27	in the thousands of place stands for the place value
10:29	to thousands . Knowing that will help us write decimal
10:33	numbers in expanded form , like the one we saw
10:35	earlier . 126.53 . The expanded form of the whole
10:40	number part is easy . We learned how to do
10:42	that in the last video 126 is 100 plus 20
10:47	plus six . But now we need to add the
10:50	fractions represented by the decimal digits to . Since there's
10:53	a five in the 10th place that stands for 5/10
10:56	. So we need to add the fraction 5/10 to
10:59	our expanded for . But we also have the digit
11:01	three and the hundreds place which stands for 300ths .
11:05	So we also need to add the fraction three over
11:08	100 to our expanded form . All right , so
11:11	that's a basic intro to decimal number of places .
11:14	There's still more to learn about them and as you
11:16	can see , decimal number of places have a lot
11:18	to do with fractions which you may not have learned
11:21	very much about yet . But that's okay . Once
11:23	you do learn more about fractions it will help decimal
11:26	number of places make even more sense . And there's
11:28	several math antics videos about fractions that can help you
11:31	with that . Like our video called converting based infractions
11:35	. The main thing is you now know how the
11:37	base 10 number system works , which is really important
11:40	since it's used all the time in math . As
11:43	always . Thanks for watching Math Antics and I'll see
11:45	you next time learn more at Math Antics dot com
00:0-1	.

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