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

Math Antics - Place Value - By Mathantics

Transcript


00:03	Uh huh . Hi I'm rob . Welcome to mathematics
00:08	. In this lesson . We're going to learn how
00:09	our basic number system works and we're going to learn
00:11	about an important concept called place value . The number
00:15	system that we use in math is called Basten because
00:18	it uses 10 different symbols for counting . Math could
00:21	use other systems that are based on a different number
00:23	like base to or base eight . But I'll give
00:26	you 10 guesses as to why the number 10 is
00:28	such a popular choice . The 10 symbols that we
00:31	use are called digits and they look like this 012345678
00:38	and nine . At first glance you might think that
00:41	that's only nine digits but remember the zero counts as
00:44	one of the digits . Also to see how our
00:46	number system uses these digits to represent amounts . Let's
00:50	pretend that we have an apple orchard full of apple
00:53	trees and each of these trees is loaded with big
00:56	, juicy red apples that we need to pick and
00:58	then count for our records . We're going to use
01:02	something called a number . Place to count . The
01:05	best way to understand a number . Place is to
01:07	imagine that it's like a small box that's only big
01:09	enough to hold one digit at a time . As
01:12	we count will change the digit that's in the number
01:14	place to match how many apples we've picked . For
01:18	example , if we start with no apples at all
01:20	, we put the digits zero in the number of
01:22	place because zero means none . But then as the
01:25	apple start coming in from the orchard , we begin
01:27	to count 12345678 and nine . Okay now we've got
01:35	nine apples but we've also got a problem . We've
01:37	already run out of digits to count with . The
01:40	highest digit we have is a nine . But there's
01:42	a lot more apples left account . What will we
01:44	do ? The solution is to use groups to help
01:47	us count . If we pick just one more apple
01:49	will have 10 . Right ? So let's combine those
01:52	10 apples into a single group . So how many
01:55	apples do we have ? 10 ? But how many
01:58	groups of 10 apples do we have ? Just one
02:02	? Does that help us with our lack of digits
02:04	? Problem . It sure does . If we use
02:06	another number place instead of using this new number ,
02:10	place to count up individual apples . One at a
02:12	time . Like we did with the first number place
02:15	we're going to use it to count apples 10 at
02:17	a time . In other words we use it to
02:19	keep track of how many groups of 10 apples that
02:21	we picked . For example , if we've picked only
02:24	one group of 10 , then we'll put the digit
02:27	one in that number of place . If we pick
02:28	two groups of 10 then we'll put the digit two
02:31	in that number of place . And if we picked
02:32	three groups of 10 then we'll put the digit three
02:35	in that number of place and so on . Do
02:37	you see what's happening ? Because the new number place
02:40	is being used to count groups of 10 . It's
02:42	allowing us to reuse our original 10 digits . But
02:45	this time they are able to count or represent bigger
02:49	amounts . Since this new number place is for counting
02:52	groups of 10 . We're going to name it the
02:54	tens place and we'll name our original number place the
02:57	ones place . Because we used it to count things
03:00	one at a time And here's the really important thing
03:03	. We're not going to use the new number place
03:05	instead of the old one . We're going to use
03:07	it alongside of the old one . So that we
03:09	have one number place for counting by ones and another
03:12	number place for counting by 10s . Using these two
03:15	number of places together lets us represent amounts that are
03:18	in between the groups of 10 . For example ,
03:20	if we've already picked 30 apples then there will be
03:23	a three in the tens place because we have three
03:25	groups of 10 but there'll be a zero in the
03:27	ones place because there are no individual apples left over
03:31	. But if we've picked 32 apples then there will
03:34	be a three in the tens place and a two
03:36	in the ones place to represent the two individual apples
03:39	that are not in the groups of 10 . In
03:42	fact using only our 10 digits and these two number
03:45	places , we can count all the way from zero
03:47	up to 99 99 . Both of our number places
03:51	are maxed out with the highest digits and we won't
03:53	be able to count any higher unless we get another
03:56	number place If we've picked 99 apples and then we
04:00	pick just one more will have exactly 100 apples .
04:04	And if we make a group from those 100 apples
04:06	we can use this new number place to count how
04:08	many groups of 100 we've picked . That means that
04:12	we can reuse the same 10 digits again in this
04:15	new number place to count how many groups of 100
04:17	we have . And you guessed it ? It's called
04:19	the hundreds place because we use it to count groups
04:22	of 100 . Are you starting to see how our
04:25	base 10 number system works ? It uses different number
04:28	of places to represent the different sized groups that we
04:31	used to count . And the digits in those number
04:33	places tell us how many of each group we have
04:36	. The digit in the ones place tells us how
04:38	many ones we have . The digit in the tens
04:40	. Place tells us how many groups of 10 we
04:43	have and the digit in the hundreds . Place tells
04:45	us how many groups of 100 we have . And
04:48	have you noticed that each time we got a new
04:50	number , place to count larger groups , we placed
04:53	it to the left of the previous number . Place
04:56	. That's important because number of places are always arranged
04:59	in the exact same order . Starting with the ones
05:02	place as you move to the left , the number
05:04	of places represent larger and larger amounts . And did
05:08	you also notice that each new number place represents groups
05:11	that are exactly 10 times bigger than the previous number
05:14	. Place 10 is 10 times bigger than one in
05:17	100 is 10 times bigger than 10 . That's really
05:20	important because it helps us see the pattern for even
05:22	bigger number of places . It helps us to see
05:25	that the next number place will count groups of 10
05:28	times 100 , which is 1000 . And that's why
05:31	it's called the thousands place . And the next number
05:33	place will count groups 10 times bigger than that .
05:36	It's the 10000s place . And the number of places
05:39	keep on going like that . Next is the 100
05:42	thousands place , then the millions place , then 10
05:45	millions , then 100 millions , then billions and so
05:50	on . Oh . And you may notice that when
05:53	we get a lot of number of places next to
05:54	each other like this , it's a little hard to
05:56	quickly recognize which places , which that's why many countries
06:00	use some kind of separator . Every three places to
06:03	make them easier to keep track of . For example
06:06	, in the US we use a comma every three
06:08	number of places to make it easier to identify things
06:11	like the thousands place or the millions place . Seeing
06:14	all these number places together helps you understand what we
06:17	mean by place value in a multi digit number .
06:20	The number place that a digit is in determines its
06:23	value . Even though we only have 10 digits ,
06:26	each digit can stand for different amounts depending on the
06:29	place that it occupies . If the digit five is
06:32	in the ones place , it just means five ,
06:35	But if a five is in the 10th place then
06:37	it means 50 . And if a five is in
06:39	the hundreds place it means 500 and it's the same
06:42	for bigger number places . A five in the 100
06:45	thousands place means 500,000 At five in the billions place
06:49	means five billion . See how a digits place affects
06:53	its value . Of course when we work with numbers
06:56	in math most of the time the number of places
06:58	are invisible but the underlying pattern is always the same
07:02	. Oh and because the number of places are invisible
07:05	in certain cases you'll need to use zeros to make
07:07	it clear what number you're talking about , To see
07:10	what I mean . Imagine that this five is in
07:12	the hundreds place to represent 500 . But if you
07:15	make the number of places invisible then it just looks
07:18	like five and not 500 . So to make sure
07:21	people know you mean 500 you need a five in
07:24	the hundreds place a zero in the tens place and
07:27	a zero in the ones place . Now you can
07:29	tell that the five is in the hundreds place and
07:31	it means 500 . Okay , now a great way
07:35	to see place value in action with some actual numbers
07:37	is to expand them to show that they're really combinations
07:40	of different groups . When we do this . It's
07:42	called writing a number and expanded form For example we
07:46	can expand 324 to be 320 and four because the
07:52	three is in the hundreds place and means 300 .
07:54	The two is in the tens place and means 20
07:57	and the four is in the ones place . So
07:58	it just means four . So 324 . An expanded
08:02	form is the combination of those amounts 300 plus 20
08:07	plus four . Let's try writing another number and expanded
08:10	for 6,715 . We can expand this into 6000 because
08:16	the six is in the thousands place Plus 700 because
08:20	the seven is in the hundreds place plus 10 because
08:23	the one is in the tens place and five because
08:26	the five is in the ones place . So the
08:29	expanded form is 6000 plus 700 plus 10 plus five
08:35	. All right . So do you see how our
08:37	base 10 number system works ? A number of places
08:40	are used to count different sized groups . Each group
08:43	is 10 times bigger than the next . And the
08:46	digits in the number of places . Tell us how
08:48	many of each group we have . The tricky part
08:51	is that the number of places are invisible . So
08:53	you have to know how they work behind the scenes
08:55	in order to make sense of multi digit numbers .
08:57	How do you like them ? Apples ? The exercises
09:02	for this section will help you practice so that you
09:04	get used to how place value works . Which is
09:06	super important if you want to be successful in math
09:09	as always . Thanks for watching Math Antics and I'll
09:12	see you next time . That gives me an idea
09:19	. I could make pies out of these , learn
09:23	more at Math Antics dot com .

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