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### Course: Arithmetic (all content)>Unit 1

Lesson 2: Ones and tens

# Intro to place value

Sal uses the number 37 to explain why we use a "ones place" and a "tens place" when writing numbers.  Created by Sal Khan.

## Want to join the conversation?

• If you just wanted to group scratches of ten together, wouldn't you leave the ones still as scratches but just change the tens to something else? Maybe an X? So it'd be `XXXIIIIIII` for thirty-seven?
• Yes, and that's essentially what Sal did, but using our already known number notation. We could call `XXXIIIIIII´: 3 X and 7 I. However, we know X represents ten I, so we call it "ten". If we have three of those tens, we join the words in a funny way and call it "thirty", then we are still left with 7 ones, which we just call seven. To join our thirty and seven we just call thirty seven (37).
• How could you become really proficient in place value?
• Practice and repetition will help a lot.
If you understand the idea of place value, you will succeed!
• Does numerals mean numbers?
• 1=I 2=II 3=III 4=IV 5=V 6=VI 7=VII 8=VIII 9=IX 10=X

• Is there a hundreds place and so on?
• Yes, in fact, there are infinity(goes on forever) places. Since numbers do not end, place values do not end. I hope this helped :)
• Are there place values in decimals?
• yes there are tenths hundredths thousandths then hundreds tens and ones
e.g 103.54= 1 thousandths 0 hundredths 3 tenths. 5 tens 4 ones
• Why doesn't Sal put the dash in the 7?
• 7's can often be confused with other number in many people's handwriting. Putting a dash in there makes it look less like a 1.
• We could have any unit to describe time then? Like a month could be a multiple of ten or 24?
• Yes. Time can be measured in multiples of seconds, minutes, hours, days, weeks, months, years, decades, centuries, millenniums . . . ok you get the idea :)
• Is it valid to say that when it comes to whole-number place value, the number value extends to the left but when dealing with decimals, the values extend from left-to-right?
• Well, if you look for a pattern...
1) Going from right to left, you'll see the place values increasing by powers of 10. So the tenths place is ten times the hundredths place, the ones place is ten times the tenths place, and so on
2) If you go from left to right, you'll see the place values decreasing by powers of 10. So tens place is one-tenth of the hundred's place, the one's place is one-tenth the tens place, and so on.
• Question: Must it always be XXXVII to equal 37, or can XXXIIIIIII and XXXIIIX also be accepted? :/
• "XXXVII" is the standard Roman Numeral form for "37." The other forms you listed do equal 37 but are not generally used due to complexity and possible confusion.
• What way would you teach a second grader the place values(ones, tens,hundreds, thousands) which they are doing in class now?
• The first time I was told of place values was very useful to me. It had these dashes that you see below:
_ _ _ _
These dashes represent the places for numbers. As you go along in life there will be more and more of these dashes which signal that there are bigger numbers out there. Starting from the right side of the dashes and going left, we see that there are 4 dashes and that each of these 4 dashes represents a place. If you were to put a seven on the first dash on the right, then you would consider 7 to be in the one's place. If you put 7 on the 3rd dash to the right then you would consider the 7 to be in the hundreds place. Please let me know if you need more assistance!

## Video transcript

Voiceover:Let's say that you wanna count the days since your last birthday because you just wanna know how long its been. And so one day after your birthday you put a mark on a wall. Then the next day you put another mark on the wall. The day after that you put another mark on the wall. So out that day you say well how many days has it been? Well you can say look there's been one, two, three days. So one way to think about it is this set of symbols right over here represents the number three. But then you keep going. The fourth day, you put another mark. Fifth day, you put another mark. And then you keep going like that day after day each day you add another mark. And this is actually the earliest way, the most basic way of representing numbers. The number is represented by the number of marks. So after bunch of days you get here and you're like on well how many days has it been? Well you just recount everything. You say one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17 days. So well you know this number representation it took me little bit of time to realize that this is 17 but it seems to be working so you just keep going. Day after day after day after day you just keep marking off the days on your wall just to sense you're counting the days since your last birthday. But at some point you realize every time you wanna know how may days its been to count it is a little bit painful. And not only that, is this is taking up a lot of space on your wall. You wish that there was an easier way to represent whatever number this is. So first of all let's just think about what number this actually is. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37. So you wish that there was a better way to represent this number which we now call 37. And maybe when you're first trying you might have even called it something called 37. You would just call it this, this number. This number of days since my birthday. And I say well look. What if there was an easier way to group the numbers? You know I have 10 fingers on my hands. What if I were to group them into 10s? And then I would say just how many groups of 10 I have and then how many ones do I have left over. Maybe that would be an easier way to represent, to represent this quantity here. And so let's do that. So one, two, three, four, five, six, seven, eight, nine, 10. So that's a group of 10 right over there. And then you have one, two, three, four, five, six, seven, eight, nine, 10. So this is another group of 10 right over here. And then let's see. We have one, two, three, four, five, six, seven, eight, nine, 10. So that is another group of 10 right over there. And then finally you have one, two, three, four, five, six, seven. So you don't get a whole group of 10 so you don't circle em. So just by doing this very simple thing now all of a sudden it's much easier to realize how many days have passed. You don't have to count everything. You just have to say okay. One group of 10. Two groups of 10. Three groups of 10. Or you can say one, two, three 10s. And so that's essentially 30. And then I have another one, two, three, four, five, six, seven. And so you say oh I have 30 and then seven if you knew to use those words which we now use. Now this is essentially what our number system does using the 10 digits we know of. The 10 digits we know of are zero, one, two, three, four, five, six, seven, eight, nine. Now what our number system allows us to do is using only these 10 digits we can essentially represent any number we want in a very quick way, a very easy way for our brains to understand it. So here if we want to represent three 10s, we would have put a three in what we would call the 10s place. We would put a three in the 10s place. And then we would put the ones, one, two, three, four, five, six, seven. We'd put the seven in the ones place. And so how do you know which place is which? Well the first place starting from the right, the first place is the ones place. And then you go one space to the left of it, you get to the 10s place. And as we'll see you go one more space you go to the 100s space. But we'll cover that in a future video. So this essentially tells us the exact same thing. This tells us the exact same thing as this does right over here. This tells us three 10s. One, two, three. Three 10s Three groups of 10. And then another set of ones. So we could rewrite this. This is equal to, this is equal to three 10s three 10s plus, plus seven ones. Or another way to think about it what are the three 10s? Well if use the same number system to represent three 10s you would write that down as 30. And then seven ones. Once again if you use our same number system you would represent that as seven. So these are all different ways of representing 37. And hopefully this allows you to appreciate how neat our number system is. Where even a number like 37 as soon as you just write scratches on a wall, it becomes pretty hard to read. And you can imagine when you get to much much larger numbers like 1,052 to have to count that many marks every time. But our number system gives us a way of dealing with it.