Regrouping with decimals: 21.3

I want to think about all of the different ways we can represent value in the number twenty twenty-one point three so one is just look straight up at the place values this two is in the tens place so it literally represents two tens so this is equal to 22 times ten this one is literally equal to 1 its 1 1 and then this 3 is 3/10 so plus 3/10 but now I want to rearrange or regroup the value in these places so for example I could take 1 from the ones place and give it to the tenths place so let's see how that would work so we're going to take 1 away from the ones place and so it's going to become a zero and we're going to give it to the tenths place and what we're going to see is that that's going to make the tens place into 13 into 13 tenths now does that actually make sense that I took one from here and it essentially added 10 to the tenths place well let's rewrite what this represents so we still have two tens so this is still going to be two tens now we have plus zero ones plus zero ones and we're essentially wanted to write that that that one that we took away from the ones place in terms of tenths so if we were to write this in terms of tents it would be ten tenths plus the three tents that were already there plus three tenths and so this is going to be equal to 13 tenths let me write that down so this is equal to 20 this is that's the color you can't see this is equal to 20 plus 0 ones so two tens plus zero ones plus 13 tens plus 13 tens let's do another example with this exact same number so once again 21 21 point 3 21 point 3 and I'll write it out again this is equal to 20 plus one plus one we'll do that in the purple color plus one plus three tenths plus three over two now I could take one from the tens place so that this only becomes this becomes just one and what do I do with that ten well let's say I give let's say with that 10 I give 9 of it to the ones place so I give 9 of it to the ones place so that this becomes 10 and I still have one left over and I give it to the tenths place so that's going to become 13 over 10 13 over 10 so what did I just do well I could rewrite this let me be clear what I did this is the same thing as this is the same thing as 1 plus 9 which you let me write it this way 1 plus which I'll write 1 plus 9 plus 1 that's obviously the same thing let me be for 10 plus 9 10 plus 9 plus 1 is the same thing as 20 and we're going to have and of course we have what we have in our ones place plus 1 plus 3/10 and what I want to do is I want to take this 9 the 9 that I took from the tens place give it to the ones place and I'm going to take this one that took from the tens place and give it to the tenths place so 1 is the same thing as 10 over 10 and so you have if you when you regroup this value you get this as being equal to 10 plus 9 plus 1 is 10 and then 10 tens plus 3/10 is 13 tenths so that's all that happened here I changed the value in the places I took 1/10 away so I'm only left I had two 10s now I only left with 1/10 and that extra 10 of value I regrouped it I gave 9 to the ones place so 1 plus 9 is 10 and then I gave one to the tenths place so 1 plus 3/10 is the same thing as 13 tenths