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what we're going to do in this video is refresh our understanding of place value but we're going to dig a little bit deeper and think about place value in the context of decimals so just as a refresher if I had the number 973 this should be review for you we already know that this rightmost space right over here this is the ones place and if we move one space to the left of that this is the tens place notice we went from ones to tens tens are ten times as much as ones and then we move one space to the left of that we go to the we multiply by tens again we get to the hundreds space and so this nine doesn't just represent nine it represents nine hundred or we could write that as nine hundred similarly the seven doesn't just represent seven it represents seven tens or 70 this 3 represents three one so it actually does represent three but as I promised we're now going to extend our end to understanding and what we do is we put a decimal here which you've probably seen before at the right and the way the reason why we even need a decimal is to really tell us where our ones place is we say okay if we go right to the left of the decimal that's going to be our one space because once we start introducing decimals we can introduce as many spaces as we want to the right of the decimal and so let's think about those a little bit if when we went from hundreds to tens notice we divided by ten when we go from tens to ones notice you divide by ten so what do you think this place over here is going to be called well what happens if you take 1/10 well then you get 1/10 so as you might imagine this is the tenths place and then if you were to go one place to the right of that what would this place be what would be tenths divided by ten or one tenth of a tenth so this would be a hundred hundreds place and then if you were to go one space to the right and we could keep doing this forever but if we were to go one space to the right of that what would it be well a hundreth divided by ten or one tenth of a hundredth is a thousand thousand space and so for example if I were to extend this number instead of it just being 973 if I were to write nine hundred seventy three point five two six what do these numbers these digits represent this five doesn't just represent five it represents it represents five tenths or another way of writing five tenths you could write it like this zero point five you just have a five in the tenths place or you could write it as five tenths this two and I think you get where this is going this doesn't just represent two it represents two hundredths I'm just going to make it very explicit in this video so it's very clear two hundredths another way to write that is you just write a two in the hundredths place so we're going one two spaces to the right of the decimal or you could write it as two over a hundred two hundredths and so you know for kicks pause the video what are all the different ways of representing this six what does this six are present well this is six thousand six thousand there's thousands there you go how would I could also write that a zero point let's use the tenths place hundredths place and then in the thousandths place I have six or I could write this as 6 over one thousand six thousands so big picture place value we can keep going to the right of the decimal and we can start representing things that are I guess you could say more precise