Hi, I’m Rob. Welcome to Math Antics. In this video, we’re going to learn about decimal place value. As that name suggests, it’s related to regular place value, so be sure to watch our video about that if you haven’t already. In that previous video, we learned how to count using just 10 different digits and number places that represent different sized groups. For example, if we needed to count 235 apples, we used different number places for counting by ones, by groups of ten, and by groups of a hundred. The digit ‘2’ in the hundreds-place represents two hundreds, the ‘3’ in the tens-place represents three tens (or thirty), and the ‘5’ in the ones-place represents five ones (or just 5). It’s a pretty amazing system if you think about it! It only has 10 digits, but those digits can be re-used in different combinations to count any number from zero, all the way to trillions of apples and beyond! But!… as amazing as it is, there’s just one little problem with our number system so far… [Crunch] What if you don’t have a whole apple? In the Place Value video, we only learned how to count whole amounts, or what we call “whole numbers”, which is the set of numbers you get if you start with 0 and then count by ones: 1,2,3,4… and so on. But, there are things besides whole amounts. It’s possible to have just part of something …like just part of an apple. And that means there are ‘in-between’ amount. You might have one apple or two apples, but you could also have something in-between that, like one and a half apples. How can the base 10 number system handle situations like that? The answer is decimal places! Decimal places are a way of extending the Base 10 number system so that it can represent amounts that are in-between whole amounts. Decimal places are just like regular number places, except that instead of using them to count GROUPS, we use them to count PARTS (or FRACTIONS) of things. To see how the Base 10 system is extended with decimal places, let’s look at the pattern of number places that we saw in the last video. We started out with a number place for counting things one at a time. And when we hit the limit of counting with it, we used another number place (on the left side of it) for counting groups of 10. By combining those two number places, we could count from zero all the way up to 99, but when we needed to count beyond that, we used another number place (on the left side of it) for counting groups of 100. And when those places were maxed out, we added a place for counting by groups of 1,000, and then by groups of 10,000 and so on. See the pattern? Each time we added a new number place, it was located to the left of the previous one, and each time it represented groups that were TEN times larger than the previous group. Since the amounts that our number places represent get bigger and bigger as we go to the left, it makes sense that number places for counting smaller amounts (like parts of something that are LESS than 1) will need to go on the right side of the ones place. That’s where the decimal places are found. And just like the whole number places can go on forever to the left, counting bigger and bigger groups, the decimal number places can go on forever to the right, counting smaller and smaller parts (or fractions). But… if number places go on forever in either direction, then how do we know which place is which? I mean… if they all look the same… or worse… if they’re invisible, then how do we know which digit goes in which place? Ah – that’s an excellent question! We do have a problem now that the number places can extend in both directions. Before, when we had only whole number places that extended in just one direction (to the left), we knew that the place that was farthest to the right was always the ones place. But now we know that number places can extend in BOTH directions, so we need a new way to tell which place is which. What we need is a point of reference… a place that we always start from. And for that, we use a special symbol called “the decimal point”, which in the United States, looks just like a period. Basically, the decimal point acts as a separator. It separates the number places that are used for counting whole values, (which are on the left side of the decimal point) from the number places that are used to count fractional values (which are on the right side of the decimal point). And that’s why you don’t see a decimal point in every number. If there’s no decimal digits in a number (like in the whole number 25), then you don’t need to show the decimal point. It’s safe to assume that the digit farthest to the right is in the ones place. Of course, you COULD still show the decimal point if you wanted to since it’s always immediately to the right of the ones place, but if there’s no decimal digits, then we don’t need to separate them from the whole number digits. If a number does have decimal digits, then we call it a “decimal number” and the decimal point helps us quickly recognize which digit is in the ones place. For example, if you see a sequence of digits like this: 1, 2, 6, point, 5, 3 You can tell right away that the digit ‘6’ is in the ones place, because it’s immediately to the left of the decimal point. And that means this ‘2’ is the tens place and this ‘1’ is in the hundreds place. Okay… but what about the digits that are to the right of the decimal point? We know that they must be in decimal number places, but what are the names of those decimal number places and what values do they count? Well, looking back at our number place pattern, we see that each time we move to the LEFT, the new number place counts amounts that are ten times BIGGER than the previous place, so each time we move to the RIGHT, that place should count amount that are ten times SMALLER than the previous place. Since the ones place counts by ‘ones’, the number place to the right of it should count by amounts that are ten times smaller than one. The amount that’s ten times smaller than one is called “a tenth”. It’s the amount you get if you take one whole (like one whole apple) and divide it into ten equal parts, keeping just one of them. One-tenth is what we call a fraction, and fractions are written using a special notation that has two numbers with a line between them. The number on the bottom tells how may equal parts a whole amount is divided into, and the top number tells you how many of those parts you have. So the fraction ‘one-tenth’ is written like this: one over ten. Getting back to our apple counting example… previously, we could only count whole apples, but now that we have a number place for counting tenths, we can count tenths of apples too. We can use the ones place and the tenths place together to count amounts that are in-between a whole number of apples. To see how it works, let’s start our counting with one whole apple and NO tenths. That means that there will be a ‘1’ in ones place and a ‘0’ in the tenths place. But now let’s start adding tenths to that. For each tenth that we count, we increase the digit in the tenths place by ‘1’ … one tenth, two tenths, three tenths, 4, 5… Let’s pause for a second to notice something important. Do you see that having 5 tenths of an apple is the same as having one-half of an apple. That’s because 5 is exactly half of 10, and the fraction 5 over 10 can be simplified to 1 over 2. That’s why having 1.5 apples is the same as having one and a half apples. Pretty cool, huh? Anyway, back to counting… 6 tenths, 7, 8, and 9 tenths. Now we have one whole apple and also nine-tenths of an apple. But our tenths place is maxed out with the digit ‘9’. That’s as high as it can count, so what do you think will happen if we add one more tenth? Yep! Those ten tenths combine to form one whole apple, and that will cause our ones place digit to increase to a ‘2’. We now have 2 whole apples (even though one is made up from slices, the amount is still equal to one whole.) See how decimal digits help us count in-between whole amount? But wait… there’s more! …more decimal number places that is. The tenths place allows us to count in between the ‘ones’, but what if we want to count amounts that are in between the ‘tenths’? [Crunch] The decimal number places keep on going to the right, and each time they count amounts that are ten times smaller than the previous amount. So if the tenths place counts fractions that are a tenth of ONE, then the next place over will count amounts that are one tenth of A TENTH! One tenth of a tenth is called ‘one hundredth’. It’s the fraction you get if you take a tenth and then divide IT into ten equal parts. It’s a very small fraction, and it’s called a hundredth because it’s the same fraction you’d get if you take a whole and divide it up into 100 parts. So its fraction form looks like this: 1 over 100. Just like tenths could be used to represent amounts that are IN-BETWEEN the ones, hundredths can be used to represent amounts that are IN-BETWEEN tenths! And just like if you combined 10 tenths, they equal one, if you combine 10 hundredths, they equal a tenth. And the decimal number places keep on going like that. The next number place over represents fractions that are one-tenth of one-hundredth. That very small fraction is called ‘one-thousandth’ because it would take 1,000 of them to make one whole. And the next place over is 10 times smaller than that; it’s called the ‘ten-thousandths’ place. And then there’s the ‘hundred-thousandths’ place… there’s the ‘millionths’ place, and so on… So do you see how truly amazing our number system is? It can represent any whole number amount, no matter how big, by adding bigger and bigger number places to the left. But it can also represent amount in between those whole amounts, with more and more precision… down to the tiniest fraction imaginable, by adding more and more decimal number places to the right. “That is truly amazing! In fact, it kinda makes my head hurt just thinkin’ about it. Of course… it could be this daw-gone pot I wear on my head all the time.” Okay, so now that you know how decimal places work. Let’s talk briefly about how we can show their place value and how we can write decimal numbers in expanded form. A digit’s value is determined by the place that it’s in. So if a ‘2’ is in tenths place… it stands for two-tenths, which can be written with the fraction ‘2 over 10’. If a ‘3’ is in the tenths place, that stands for three-tenths or ‘3 over 10’. If a ‘4’ is in the tenths place, that stands for four-tenths or ‘4 over 10’, and so on… And just like a ‘2’ in the tenths place stands for the place value ‘two-tenths’, a ‘2’ in the hundredths place stands for the place value ‘two-hundredths’ and a ‘2’ in the thousandths place stands for the place value ‘two-thousandths’. Knowing that will help us write decimal numbers in expanded form… like the one we saw earlier: 126.53. The expanded form of the whole number part is easy. We learned how to do that in the last video: 126 is 100 + 20 + 6 But now we need to add the fractions represented by the decimal digits too. Since there’s a ‘5’ in the tenths place, that stands for five-tenths, so we need to add the fraction ‘5 over 10’ to our expanded form. But we also have the digit ‘3’ in the hundredths place which stands for three-hundredths, so we also need to add the fraction ‘3 over 100’ to our expanded form. Alright… so that’s a basic intro to decimal number places. There’s still more to learn about them and as you can see, decimal number places have a lot to do with fractions, which you may not have learned very much about yet. But that’s okay. Once you do learn more about fractions, it will help decimal number places make even more sense. And there’s several Math Antics videos about fractions that can help you with that, like our video called “Converting Base-10 Fractions”. The main thing is you now know how the Base 10 number system works, which is really important since it’s used all the time in math. As always, thanks for watching Math Antics and I’ll see ya next time. Learn more at www.mathantics.com

You are better than my maths teacher

Subscribe me 4 a few subscribers

thanks for the help

am glad thairs pepole like you my techer dosn't like to explane stuff 2 times so i just watch your vids

I like post malone's channel better than yours

You are good at math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

??

https://www.youtube.com/watch?v=KG6ILNOiMg

idk why but my teacher always watch your videos ? she does not teach?!?

This really helped me in school thank you for making this video

You are the best teacher I mean teachers that teach me in school for 6 hours and can't explain like you

you helped me to study now i can play Fortnite and robloxs

idk y whenever a

teacher teachus anything the lesson still need to have someapplesin it LolWork at iprep school 8

Hahahahh is it funny someone took his apple ???????????????

Lol i love all your vids

MathAntics!!

Bet this guy went to college then university

this make easy to explain to my little brother. Thank you maked math so fun to learn

He is smart ??

NERDZ!

Therefore 1 ≠ to 0.999…

LOL

this guy is better than my maths teacher.

? for apples!

Guys you know when ur teacher shows u math antics of the math lesson, well I know why they do it. There to lazy to teach us?

i wish I will get a good grade from decimal place value. thank for help me .??☺??

7:10 1 is equal to 2

– –

2. 4

you are just so amazing. its much easy and understandable now. I wanna say a heartiest thanks.

clearly understood

Thank you!you make it so much easier for me to study ?

This is kiwi

?

One like=one dollar for kiwi

To buy food he needs 5 dollars

To buy a house he needs 1000 dollars

And he needs food everyday

But if he has a house then he needs food every 5 days

I like it. make meme now!!!!!!!!!!!!!!!!!!!!! Funny 'take the apple meme!' parts!

did u have a twin brother???

very helpful thank you

cool

hi jaiyanna

thanks man your the best

It plops

I GOT 25 OUT OF 25 FULL MARKS i got that full marks because of learning from this VIDEO

helloyoutube

U are legendary !!!

idc if this is late, you helped me with my tests, so grateful for your help, thank you!

Are you a teacher

The green grape has left the chatRoses are red

Voilets aren't blue

Please like me comment wait…

?Why is this blue?

You man are wet blad

hi

OMG NEXT WEEK IS EQAO IN TORONTO!

It is very good boy and

ji

How in the world do you only have 1M subs you should have like 10M

god bless mathantics

Hi i am omani and my name is noor al mahrooqi I loved the vidoe

hacker beware!

pogchamp

She are good teacher of math

Where dislike from??

Hello u help me sooooòooooooooooooooooooooo much??????? but i hope it helps me in test???

One thing i would like to say is that i loooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooove cats soooooo much .??????i like cats more than anyone else don't say no or else?

why dont you teach in school

in my school

subcribe to him if u think he is better than your teacher……………

I love maths like you. Do you like maths like me? You are the best mathematicians.And you are the best maths teacher in the world can you teach when dose the number’s stop.

Why do we need to learn maths if we have him.

it is good comments

Thanks Rob if you were my school teacher i will understand every thing our teacher is dumb

Johnny Appleton?

BAD VIDE

plzzz… post a video on comparing decimals

on need school just watch him as we are in the home like home schooling muahahahah no need school~~~~~`

Your the best person to explain thanks so much!

Can i request of acceleration? ?

Can u pls make a binary video?

Math antics make it easy and fun learning. My teacher and my classmates loved Math antics. And he makes it seem its easy. Plz be my math teacher!!

I love your decimal teaching !!!!!!!!!☺????✅✅✅

Thank you math antics brom???

Mathantics always saves when I'm in trouble with Math.One time,I searched my lesson in YouTube and I found Mathantics,I watched it then I know how to do it.They make my lessons a lot more easier.Thanks to Mathantics

Im only watching this because of my dad

#ilovemathantics

Adaniy la poo poo

my kids said that you're cringe i absoluty dont know what that means so i guess they said you're amzaing thx just subed

Why is every body is just saying OmG YoUreeE sO NiCeeE owwww or thAnkk YoU FoR teachInG

thanks for the info

I DID NOT UNDERSTAND ANYTHING▪

gooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooddd

thank you so much sir, ^_^

You have all I need in math subject yoy are amazing like if it is true

Your the best math teacher ever

Sir your Maths working out Is amazing

You are amaizing thank you .

some teachers watches thiswow this guy is right like if its real????????

I'm glad you have translated it in foreign languages so people worldwide can use it. I started to watch your videos in Norwegian! ?

My teacher with put these videos on and when she was done with this video she said, “well ok, I didn’t know that”

This helped me! Since I dont like asking for help from my teacher!TwT

Yeah

wow this helped me alot

Wtfrick

??

This 77 4

??????